MathsGee Q&A - Recent questions tagged plane
https://mathsgee.com/tag/plane
Powered by Question2AnswerMeasures of lines and angles
https://mathsgee.com/39971/measures-of-lines-and-angles
<p>Measures of lines and angles</p>
<p> </p>
<iframe src="https://mathsgee.com/learn/mod/hvp/embed.php?id=14145" width="100%" height="256" frameborder="0" allowfullscreen="allowfullscreen" title="measures of lines and angles"></iframe><script src="https://mathsgee.com/learn/mod/hvp/library/js/h5p-resizer.js" charset="UTF-8"></script>
<p> </p>Mathematicshttps://mathsgee.com/39971/measures-of-lines-and-anglesMon, 23 May 2022 17:16:58 +0000Determine the value(s) of \(x\) and \(y\) :
https://mathsgee.com/39332/determine-the-value-s-of-x-and-y
<p>Determine the value(s) of \(x\) and \(y\) :</p>
<p><img alt="values" src="https://mathsgee.com/?qa=blob&qa_blobid=11062796726814948457" style="height:177px; width:252px"></p>Mathematicshttps://mathsgee.com/39332/determine-the-value-s-of-x-and-ySun, 17 Apr 2022 06:55:30 +0000Determine the value of \(x\)
https://mathsgee.com/39330/determine-the-value-of-x
<p>Determine the value of \(x\) :</p>
<p><img alt="circle 2" src="https://mathsgee.com/?qa=blob&qa_blobid=228899636979419711" style="height:151px; width:228px"></p>Mathematicshttps://mathsgee.com/39330/determine-the-value-of-xSun, 17 Apr 2022 06:53:01 +0000What is local maxima/minima in differentiation and calculus?
https://mathsgee.com/38090/what-is-local-maxima-minima-in-differentiation-and-calculus
What is local maxima/minima in differentiation and calculus?Mathematicshttps://mathsgee.com/38090/what-is-local-maxima-minima-in-differentiation-and-calculusSun, 20 Feb 2022 01:53:39 +0000Determine the sum of \(x^{4}\) and \(x^{4}-3 x y+y^{2}\) and \(-3 x^{4}+7 x y+10 y^{2}\)
https://mathsgee.com/37549/determine-the-sum-of-x-4-and-x-4-3-x-y-y-2-and-3-x-4-7-x-y-10-y-2
Determine the sum of \(x^{4}\) and \(x^{4}-3 x y+y^{2}\) and \(-3 x^{4}+7 x y+10 y^{2}\)Mathematicshttps://mathsgee.com/37549/determine-the-sum-of-x-4-and-x-4-3-x-y-y-2-and-3-x-4-7-x-y-10-y-2Sat, 05 Feb 2022 08:07:04 +0000A is a transformed object to image A'. Mention two types of transformation that took place.
https://mathsgee.com/37524/transformed-object-image-mention-types-transformation-place
<p>A is a transformed object to image A'. Mention two types of transformation that took place.</p>
<p><img alt="cvc" src="https://mathsgee.com/?qa=blob&qa_blobid=17611742837935888733" style="height:154px; width:256px"></p>Mathematicshttps://mathsgee.com/37524/transformed-object-image-mention-types-transformation-placeSat, 05 Feb 2022 05:47:57 +0000Given the parametric curve \[ x=\cos ^{3} t, y=\sin ^{3} t \]
https://mathsgee.com/37372/given-the-parametric-curve-x-cos-3-t-y-sin-3-t
Given the parametric curve<br />
\[<br />
x=\cos ^{3} t, y=\sin ^{3} t<br />
\]<br />
<br />
(a) Without eliminating the parameter \(t\), show that \(\frac{d y}{d x}=-\tan t\).<br />
(b) Determine the concavity of this curve when \(t=1\).Mathematicshttps://mathsgee.com/37372/given-the-parametric-curve-x-cos-3-t-y-sin-3-tFri, 04 Feb 2022 11:40:31 +0000This question concerns the parametric curve \(x=t^{3}-4 t, y=2 t^{2}-4 t,-\infty<\) \(t<\infty\).
https://mathsgee.com/37364/this-question-concerns-the-parametric-curve-t-3-infty-infty
This question concerns the parametric curve \(x=t^{3}-4 t, y=2 t^{2}-4 t,-\infty<\) \(t<\infty\).<br />
<br />
(a) Which of the two graphs on Figure \(4.4\) corresponds to the given parametric curve?<br />
(b) Find the \(y\)-coordinates of all points where the curve crosses the \(y\)-axis.<br />
(c) This curve crosses itself at exactly one point. Find equations of both tangent lines at that point.Mathematicshttps://mathsgee.com/37364/this-question-concerns-the-parametric-curve-t-3-infty-inftyFri, 04 Feb 2022 11:32:20 +0000Consider the parametric curve \(x(t)=-2+2 \cos t, y(t)=1-2 \sin t\)
https://mathsgee.com/37363/consider-the-parametric-curve-x-t-2-2-cos-t-y-t-1-2-sin-t
Consider the parametric curve \(x(t)=-2+2 \cos t, y(t)=1-2 \sin t\).<br />
<br />
(a) State the Cartesian equation of the curve and the sketch the curve. Determine the direction of evolution of the curve for increasing \(t\) and indicate it on the graph.<br />
(b) Find the points on the curve for which the tangent line has a slope of \(1 .\)Mathematicshttps://mathsgee.com/37363/consider-the-parametric-curve-x-t-2-2-cos-t-y-t-1-2-sin-tFri, 04 Feb 2022 11:31:29 +0000The parametric equations for a curve are given by \[ x=\theta-\sin \theta, \quad y=1-\cos \theta \]
https://mathsgee.com/37362/parametric-equations-curve-given-theta-theta-quad-cos-theta
The parametric equations for a curve are given by<br />
\[<br />
x=\theta-\sin \theta, \quad y=1-\cos \theta<br />
\]<br />
<br />
(a) Find \(\frac{d x}{d y}\) as a function of \(\theta\).<br />
(b) Find \(\frac{d^{2} x}{d y^{2}}\) as a function of \(\theta\).<br />
(c) Find the tangent line to the curve at the point of the curve obtained by setting \(\theta=\frac{\pi}{3}\).Mathematicshttps://mathsgee.com/37362/parametric-equations-curve-given-theta-theta-quad-cos-thetaFri, 04 Feb 2022 11:30:24 +0000Let \(x=2 \sin t+1\) and \(y=2 t^{3}-3\) define a parametric curve. Find \(\frac{d^{2} y}{d x^{2}}\) as a function of \(t\), without simplifying your answer.
https://mathsgee.com/37360/define-parametric-curve-function-without-simplifying-answer
Let \(x=2 \sin t+1\) and \(y=2 t^{3}-3\) define a parametric curve. Find \(\dfrac{d^{2} y}{d x^{2}}\) as a function of \(t\), without simplifying your answer.Mathematicshttps://mathsgee.com/37360/define-parametric-curve-function-without-simplifying-answerFri, 04 Feb 2022 11:28:36 +0000The trajectory of a particle in a plane as a function of the time \(t\) in seconds is given by the parametric equations \[ x=3 t^{2}+2 t-3, \quad y=2 t^{3}+2 . \]
https://mathsgee.com/37359/trajectory-particle-function-seconds-parametric-equations
The trajectory of a particle in a plane as a function of the time \(t\) in seconds is given by the parametric equations<br />
\[<br />
x=3 t^{2}+2 t-3, \quad y=2 t^{3}+2 .<br />
\]<br />
Prove that there is exactly one time when the particle crosses the line \(y=x\).Mathematicshttps://mathsgee.com/37359/trajectory-particle-function-seconds-parametric-equationsFri, 04 Feb 2022 11:27:50 +0000If \(x^{5}+y^{5}=1\), what is \(y^{\prime}\) in terms of \(x\) and \(y\) ?
https://mathsgee.com/37331/if-x-5-y-5-1-what-is-y-prime-in-terms-of-x-and-y
If \(x^{5}+y^{5}=1\), what is \(y^{\prime}\) in terms of \(x\) and \(y\) ?Mathematicshttps://mathsgee.com/37331/if-x-5-y-5-1-what-is-y-prime-in-terms-of-x-and-yFri, 04 Feb 2022 09:56:43 +0000Explain carefully why the equation \[ 4 x-2+\cos \left(\frac{\pi x}{2}\right)=0 \] has exactly one real root.
https://mathsgee.com/37325/explain-carefully-equation-left-frac-right-exactly-real-root
Explain carefully why the equation<br />
\[<br />
4 x-2+\cos \left(\frac{\pi x}{2}\right)=0<br />
\]<br />
has exactly one real root.Mathematicshttps://mathsgee.com/37325/explain-carefully-equation-left-frac-right-exactly-real-rootFri, 04 Feb 2022 09:51:42 +0000The equation of position vs. time for a moving object, in SI units, is as \(x=-t^{2}+6 t-9 .\) Which of the following choices are correct?
https://mathsgee.com/36806/equation-position-moving-object-following-choices-correct
The equation of position vs. time for a moving object, in SI units, is as \(x=-t^{2}+6 t-9 .\) Which of the following choices are correct?<br />
<br />
(a) The object's acceleration is constant and its magnitude is \(1 \mathrm{~m} / \mathrm{s}^{2}\).<br />
(b) The object's velocity at the initial time \(t=0\) is to the negative \(x\)-axis.<br />
(c) The object's initial position is on the negative side of the \(x\)-axis.Physics & Chemistryhttps://mathsgee.com/36806/equation-position-moving-object-following-choices-correctWed, 26 Jan 2022 06:59:01 +0000If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.
https://mathsgee.com/36682/the-sum-three-vectors-zero-must-they-lie-the-same-plane-explain
If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.Mathematicshttps://mathsgee.com/36682/the-sum-three-vectors-zero-must-they-lie-the-same-plane-explainWed, 26 Jan 2022 00:21:17 +0000In \(\mathbb{R}^{4}\), compute the distance from the point \((1,-2,0,3)\) to the hyperplane \(x_{1}+3 x_{2}-\) \(x_{3}+x_{4}=3\).
https://mathsgee.com/36452/mathbb-compute-the-distance-from-the-point-to-the-hyperplane
In \(\mathbb{R}^{4}\), compute the distance from the point \((1,-2,0,3)\) to the hyperplane \(x_{1}+3 x_{2}-\) \(x_{3}+x_{4}=3\).Mathematicshttps://mathsgee.com/36452/mathbb-compute-the-distance-from-the-point-to-the-hyperplaneFri, 21 Jan 2022 08:20:07 +0000In \(\mathbb{R}^{3}\), let \(N\) be a non-zero vector and \(X_{0}\) and \(Z\) points.
https://mathsgee.com/36440/in-mathbb-r-3-let-n-be-a-non-zero-vector-and-x-0-and-z-points
In \(\mathbb{R}^{3}\), let \(N\) be a non-zero vector and \(X_{0}\) and \(Z\) points.<br />
a) Find the equation of the plane through the origin that is orthogonal to \(N\), so \(N\) is a normal vector to this plane.<br />
b) Compute the distance from the point \(Z\) to the origin.<br />
c) Find the equation of the plane parallel to the above plane that passes through the point \(X_{0}\).<br />
d) Find the distance between the parallel planes in parts a) and c).<br />
e) Let \(S\) be the sphere centered at \(Z\) with radius \(r\). For which value(s) of \(r\) is this sphere tangent to the plane in part c)?Mathematicshttps://mathsgee.com/36440/in-mathbb-r-3-let-n-be-a-non-zero-vector-and-x-0-and-z-pointsFri, 21 Jan 2022 08:09:05 +0000Let \(V, W\) be vectors in the plane \(\mathbb{R}^{2}\) with lengths \(\|V\|=3\) and \(\|W\|=5 .\) What are the maxima and minima of \(\|V+W\| ?\) When do these occur?
https://mathsgee.com/36434/vectors-plane-mathbb-lengths-what-maxima-minima-these-occur
Let \(V, W\) be vectors in the plane \(\mathbb{R}^{2}\) with lengths \(\|V\|=3\) and \(\|W\|=5 .\) What are the maxima and minima of \(\|V+W\| ?\) When do these occur?Mathematicshttps://mathsgee.com/36434/vectors-plane-mathbb-lengths-what-maxima-minima-these-occurFri, 21 Jan 2022 08:03:32 +0000Find all linear maps \(L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) whose kernel is exactly the plane \(\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathbb{R}^{3} \mid\right.\) \(\left.x_{1}+2 x_{2}-x_{3}=0\right\}\)
https://mathsgee.com/36346/linear-mathbb-rightarrow-mathbb-kernel-exactly-mathbb-right
Find all linear maps \(L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) whose kernel is exactly the plane \(\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathbb{R}^{3} \mid\right.\) \(\left.x_{1}+2 x_{2}-x_{3}=0\right\}\)Mathematicshttps://mathsgee.com/36346/linear-mathbb-rightarrow-mathbb-kernel-exactly-mathbb-rightFri, 21 Jan 2022 01:10:37 +0000Linear maps \(F(X)=A X\), where \(A\) is a matrix, have the property that \(F(0)=A 0=0\), so they necessarily leave the origin fixed. It is simple to extend this to include a translation,
https://mathsgee.com/36345/matrix-property-necessarily-simple-extend-include-translation
<p>Linear maps \(F(X)=A X\), where \(A\) is a matrix, have the property that \(F(0)=A 0=0\), so they necessarily leave the origin fixed. It is simple to extend this to include a translation,
<br>
\[
<br>
F(X)=V+A X,
<br>
\]
<br>
where \(V\) is a vector. Note that \(F(0)=V\).
<br>
Find the vector \(V\) and the matrix \(A\) that describe each of the following mappings [here the light blue \(F\) is mapped to the dark red \(F]\).</p>
<p><img alt="trans" src="https://mathsgee.com/?qa=blob&qa_blobid=6701903781535952344" style="height:547px; width:600px"></p>Mathematicshttps://mathsgee.com/36345/matrix-property-necessarily-simple-extend-include-translationFri, 21 Jan 2022 01:09:58 +0000Find a linear map of the plane, \(A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) that does the following transformation of the letter \(\mathbf{F}\) (here the smaller \(\mathbf{F}\) is transformed to the larger one):
https://mathsgee.com/36344/rightarrow-following-transformation-smaller-transformed
<p>a). Find a linear map of the plane, \(A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) that does the following transformation of the letter \(\mathbf{F}\) (here the smaller \(\mathbf{F}\) is transformed to the larger one):</p>
<p> </p>
<p><img alt="transformation" src="https://mathsgee.com/?qa=blob&qa_blobid=11627696595037809159" style="height:274px; width:421px"></p>
<p>b). Find a linear map of the plane that inverts this map, that is, it maps the larger \(\mathbf{F}\) to the smaller.</p>Mathematicshttps://mathsgee.com/36344/rightarrow-following-transformation-smaller-transformedFri, 21 Jan 2022 01:08:03 +0000Proof or counterexample. In these \(L\) is a linear map from \(\mathbb{R}^{2}\) to \(\mathbb{R}^{2}\), so its representation will be as a \(2 \times 2\) matrix.
https://mathsgee.com/36331/counterexample-linear-mathbb-mathbb-representation-matrix
Proof or counterexample. In these \(L\) is a linear map from \(\mathbb{R}^{2}\) to \(\mathbb{R}^{2}\), so its representation will be as a \(2 \times 2\) matrix.<br />
<br />
<br />
<br />
a) If \(L\) is invertible, then \(L^{-1}\) is also invertible.<br />
b) If \(L V=5 V\) for all vectors \(V\), then \(L^{-1} W=(1 / 5) W\) for all vectors \(W\).<br />
c) If \(L\) is a rotation of the plane by 45 degrees counterclockwise, then \(L^{-1}\) is a rotation by 45 degrees clockwise.<br />
d) If \(L\) is a rotation of the plane by 45 degrees counterclockwise, then \(L^{-1}\) is a rotation by 315 degrees counterclockwise.<br />
e) The zero map \((0 \mathbf{V}=0\) for all vectors \(\mathbf{V})\) is invertible.<br />
f) The identity map ( \(I \mathbf{V}=\mathbf{V}\) for all vectors \(\mathbf{V}\) ) is invertible.<br />
g) If \(L\) is invertible, then \(L^{-1} 0=0\).<br />
h) If \(L \mathbf{V}=0\) for some non-zero vector \(\mathbf{V}\), then \(L\) is not invertible.<br />
i) The identity map (say from the plane to the plane) is the only linear map that is its own inverse: \(L=L^{-1}\).Mathematicshttps://mathsgee.com/36331/counterexample-linear-mathbb-mathbb-representation-matrixFri, 21 Jan 2022 00:54:49 +0000Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
https://mathsgee.com/36330/find-a-real-2-times-2-matrix-a-other-than-a-i-such-that-a-5-i
Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).Mathematicshttps://mathsgee.com/36330/find-a-real-2-times-2-matrix-a-other-than-a-i-such-that-a-5-iFri, 21 Jan 2022 00:53:48 +0000Find a \(3 \times 3\) matrix \(A\) mapping \(\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) that rotates the \(x_{1} x_{3}\) plane by 60 degrees and leaves the \(x_{2}\) axis fixed.
https://mathsgee.com/36328/matrix-mapping-mathbb-rightarrow-mathbb-rotates-degrees-leaves
Find a \(3 \times 3\) matrix \(A\) mapping \(\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) that rotates the \(x_{1} x_{3}\) plane by 60 degrees and leaves the \(x_{2}\) axis fixed.Mathematicshttps://mathsgee.com/36328/matrix-mapping-mathbb-rightarrow-mathbb-rotates-degrees-leavesFri, 21 Jan 2022 00:52:19 +0000Find a \(3 \times 3\) matrix that acts on \(\mathbb{R}^{3}\) as follows: it keeps the \(x_{1}\) axis fixed but rotates the \(x_{2} x_{3}\) plane by 60 degrees.
https://mathsgee.com/36327/times-matrix-mathbb-follows-keeps-fixed-rotates-plane-degrees
Find a \(3 \times 3\) matrix that acts on \(\mathbb{R}^{3}\) as follows: it keeps the \(x_{1}\) axis fixed but rotates the \(x_{2} x_{3}\) plane by 60 degrees.Mathematicshttps://mathsgee.com/36327/times-matrix-mathbb-follows-keeps-fixed-rotates-plane-degreesFri, 21 Jan 2022 00:51:48 +0000Find the inverse to a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
https://mathsgee.com/36326/inverse-rotates-degrees-degrees-degrees-counterclockwise
Find the inverse to a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).Mathematicshttps://mathsgee.com/36326/inverse-rotates-degrees-degrees-degrees-counterclockwiseFri, 21 Jan 2022 00:51:00 +0000Find a matrix that rotates the plane through \(+60\) degrees, keeping the origin fixed.
https://mathsgee.com/36325/matrix-rotates-plane-through-degrees-keeping-origin-fixed
Find a matrix that rotates the plane through \(+60\) degrees, keeping the origin fixed.Mathematicshttps://mathsgee.com/36325/matrix-rotates-plane-through-degrees-keeping-origin-fixedFri, 21 Jan 2022 00:49:44 +0000Find a \(2 \times 2\) matrix that reflects across the horizontal axis followed by a rotation the plane by \(+45\) degrees.
https://mathsgee.com/36324/matrix-reflects-across-horizontal-followed-rotation-degrees
Find a \(2 \times 2\) matrix that reflects across the horizontal axis followed by a rotation the plane by \(+45\) degrees.Mathematicshttps://mathsgee.com/36324/matrix-reflects-across-horizontal-followed-rotation-degreesFri, 21 Jan 2022 00:49:14 +0000Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees followed by a reflection across the horizontal axis.
https://mathsgee.com/36323/matrix-rotates-degrees-followed-reflection-across-horizontal
Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees followed by a reflection across the horizontal axis.Mathematicshttps://mathsgee.com/36323/matrix-rotates-degrees-followed-reflection-across-horizontalFri, 21 Jan 2022 00:48:09 +0000Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
https://mathsgee.com/36322/matrix-rotates-degrees-degrees-degrees-counterclockwise
Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).Mathematicshttps://mathsgee.com/36322/matrix-rotates-degrees-degrees-degrees-counterclockwiseFri, 21 Jan 2022 00:47:41 +0000Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if \[ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \]
https://mathsgee.com/35949/determine-frac-mathrm-d-y-mathrm-d-x-if-y-left-x-2-frac-1-x-2-right
Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if<br />
\[<br />
y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}<br />
\]Mathematicshttps://mathsgee.com/35949/determine-frac-mathrm-d-y-mathrm-d-x-if-y-left-x-2-frac-1-x-2-rightSat, 15 Jan 2022 03:12:55 +0000How do I determine the equation of a normal in $R^2$ or $R^3$?
https://mathsgee.com/35834/how-do-i-determine-the-equation-of-a-normal-in-r-2-or-r-3
How do I determine the equation of a normal in $R^2$ or $R^3$?Mathematicshttps://mathsgee.com/35834/how-do-i-determine-the-equation-of-a-normal-in-r-2-or-r-3Thu, 13 Jan 2022 08:50:45 +0000What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
https://mathsgee.com/35816/what-the-distance-d-between-the-point-left-right-line-0in
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$Mathematicshttps://mathsgee.com/35816/what-the-distance-d-between-the-point-left-right-line-0inThu, 13 Jan 2022 08:32:51 +0000Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
https://mathsgee.com/35814/prove-that-the-distance-d-between-the-point-left-right-plane
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is $$ D=\frac{\left|a x_{0}+b y_{0}+c z_{0}+d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} $$Mathematicshttps://mathsgee.com/35814/prove-that-the-distance-d-between-the-point-left-right-planeThu, 13 Jan 2022 08:31:09 +0000Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
https://mathsgee.com/35812/find-the-distance-d-between-the-point-4-3-and-the-plane-2-1
Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.Mathematicshttps://mathsgee.com/35812/find-the-distance-d-between-the-point-4-3-and-the-plane-2-1Thu, 13 Jan 2022 08:29:41 +0000Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
https://mathsgee.com/35807/do-the-points-and-form-the-vertices-of-right-triangle-explain
Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.Mathematicshttps://mathsgee.com/35807/do-the-points-and-form-the-vertices-of-right-triangle-explainThu, 13 Jan 2022 08:25:35 +0000A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?
https://mathsgee.com/35804/sailboat-travels-mathrm-exerts-force-mathrm-toward-northeast
A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?Mathematicshttps://mathsgee.com/35804/sailboat-travels-mathrm-exerts-force-mathrm-toward-northeastThu, 13 Jan 2022 08:23:17 +0000The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
https://mathsgee.com/35780/the-distance-from-the-point-1-to-the-plane-2-x-10-11-is-equal-to
The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to<br />
<br />
<br />
<br />
A) $\dfrac{1}{3}$<br />
<br />
B) 3<br />
<br />
C) $\dfrac{1}{15}$<br />
<br />
D) 5<br />
<br />
E) none of the aboveMathematicshttps://mathsgee.com/35780/the-distance-from-the-point-1-to-the-plane-2-x-10-11-is-equal-toThu, 13 Jan 2022 07:55:41 +0000Determine whether planes $2 x+y+z-1=0,-x+3 y-2 z-3=0$ and $3 x-y=-1$ intersect. If yes, find the intersection.
https://mathsgee.com/35775/determine-whether-planes-intersect-find-the-intersection
Determine whether planes $2 x+y+z-1=0,-x+3 y-2 z-3=0$ and $3 x-y=-1$ intersect. If yes, find the intersection.Mathematicshttps://mathsgee.com/35775/determine-whether-planes-intersect-find-the-intersectionThu, 13 Jan 2022 07:51:06 +0000Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.
https://mathsgee.com/35774/find-the-equation-plane-that-contains-z-axis-and-the-point
Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.Mathematicshttps://mathsgee.com/35774/find-the-equation-plane-that-contains-z-axis-and-the-pointThu, 13 Jan 2022 07:50:19 +0000Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$
https://mathsgee.com/35750/which-the-following-the-equation-the-plane-through-the-points
Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$ \begin{equation} \text { A. }\left|\begin{array}{rrr} x-3 & y+2 & z-5 \\ 2 & 6 & -6 \\ -1 & -4 & 2 \end{array}\right|=0 \end{equation} $$ \text { B. } x(3,-2,5)+y(1,4,-1)+z(2,-6,7)=0 $$ \begin{equation} \text { C. }\left|\begin{array}{rrr} x-1 & y-4 & z+1 \\ 2 & 6 & -6 \\ -1 & -4 & 2 \end{array}\right|=0 \end{equation} $$ \text { D. }(3,-2,5)=p(1,4,-1)-(2,-6,7), p \in \mathbf{R} $$ \begin{equation} \text { E. }\left|\begin{array}{rrr} x-1 & y-4 & z+1 \\ 1 & -3 & 3 \\ 1 & -10 & 8 \end{array}\right|=0 \end{equation}Mathematicshttps://mathsgee.com/35750/which-the-following-the-equation-the-plane-through-the-pointsThu, 13 Jan 2022 07:03:19 +0000Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$
https://mathsgee.com/35747/which-following-equation-which-passes-through-contains-mathrm
Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$<br />
<br />
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<br />
A. there are infinitely many such planes<br />
<br />
B. $r=(-3,4,-3)+p(-2,1,5), p \in \mathrm{R}$<br />
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C. $-2 x+6 y=2 z+36$<br />
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D. $-3 x+4 y-3 z=2$<br />
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E. $-x-2 y+5=0$Mathematicshttps://mathsgee.com/35747/which-following-equation-which-passes-through-contains-mathrmThu, 13 Jan 2022 06:56:29 +0000Which of the following is the unit vector in direction of $a \times b$ if $a=(2,1,1)$ and $b=(-1,2,2) ?$
https://mathsgee.com/35746/which-the-following-the-unit-vector-direction-times-a-and-b
Which of the following is the unit vector in direction of $a \times b$ if $a=(2,1,1)$ and $b=(-1,2,2) ?$<br />
<br />
<br />
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A. $\left(-\frac{1}{2}, \frac{1}{2}, 0\right)$<br />
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B. $(0,-1,1)$<br />
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C. $\left(0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$<br />
<br />
D. $(0,1,0)$<br />
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E. $(0,-5,5)$Mathematicshttps://mathsgee.com/35746/which-the-following-the-unit-vector-direction-times-a-and-bThu, 13 Jan 2022 06:55:14 +0000The distance from the point $(-1,1,1)$ to the plane
https://mathsgee.com/35734/the-distance-from-the-point-1-1-1-to-the-plane
The distance from the point $(-1,1,1)$ to the plane $$ 2 x-10 y+11 z-4=0 $$ is equal to<br />
<br />
<br />
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A) 3<br />
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B) $\frac{1}{3}$<br />
<br />
C) 5<br />
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D) $\frac{1}{5}$<br />
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E) none of the aboveMathematicshttps://mathsgee.com/35734/the-distance-from-the-point-1-1-1-to-the-planeThu, 13 Jan 2022 06:37:20 +0000Write the equation of the plane through the points $ (3,-2,5),(1,4,-1),(2,-6,7) $
https://mathsgee.com/35729/write-the-equation-of-the-plane-through-the-points-3-5-1-4-1-2-6-7
Write the equation of the plane through the points $$ (3,-2,5),(1,4,-1),(2,-6,7) $$Mathematicshttps://mathsgee.com/35729/write-the-equation-of-the-plane-through-the-points-3-5-1-4-1-2-6-7Thu, 13 Jan 2022 06:33:15 +0000Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.
https://mathsgee.com/35688/substitution-otherwise-general-solution-differential-equation
Consider the differential equation $\frac{d x}{d y}=\frac{y^{2}+y^{2} e^{\left(\frac{x}{y}\right)^{2}}+2 x^{2} e^{\left(\frac{x}{y}\right)^{2}}}{2 x y e^{\left(\frac{x}{y}\right)^{2}}}$ Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.Mathematicshttps://mathsgee.com/35688/substitution-otherwise-general-solution-differential-equationThu, 13 Jan 2022 05:23:42 +0000Find the particular solution of the differential equation given that $y=1$ when $x=0$.
https://mathsgee.com/35687/find-particular-solution-differential-equationgiven-that
Find the particular solution of the differential equation given that $y=1$ when $x=0$.<br />
<br />
<br />
<br />
NB: $\dfrac{d x}{d y}=\dfrac{y^{2}+y^{2} e^{\left(\frac{x}{y}\right)^{2}}+2 x^{2} e^{\left(\frac{x}{y}\right)^{2}}}{2 x y e^{\left(\frac{x}{y}\right)^{2}}}$Mathematicshttps://mathsgee.com/35687/find-particular-solution-differential-equationgiven-thatThu, 13 Jan 2022 05:22:38 +0000The particular solution of the differential equation $\frac{d y}{d x}=\frac{\cos x}{x^{2}}-\frac{2 y}{x}$ under the initial conditions $x=\pi$ and $y=1$ is
https://mathsgee.com/35676/particular-solution-differential-equation-initial-conditions
The particular solution of the differential equation $\dfrac{d y}{d x}=\dfrac{\cos x}{x^{2}}-\dfrac{2 y}{x}$ under the initial conditions $x=\pi$ and $y=1$ is<br />
<br />
<br />
<br />
A. $y=\frac{\sin x-\pi^{2}}{x^{2}}$<br />
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<br />
<br />
B. $y=\frac{\pi^{2}-\sin x}{x^{2}}$<br />
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C. $\quad y=\frac{\sin x+\pi^{2}}{x^{2}}$<br />
<br />
<br />
<br />
D. $\quad y=-\frac{\sin x+\pi^{2}}{x^{2}}$<br />
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<br />
<br />
E. None of theseMathematicshttps://mathsgee.com/35676/particular-solution-differential-equation-initial-conditionsThu, 13 Jan 2022 03:38:43 +0000Show that $\cos x$ is the integrating factor of the linear differential equation $\cos x \frac{d y}{d x}=1+y \sin x$ where $\left(-\frac{\pi}{2}<x<\frac{\pi}{2}\right) .$
https://mathsgee.com/35656/integrating-factor-linear-differential-equation-where-right
Show that $\cos x$ is the integrating factor of the linear differential equation $\cos x \frac{d y}{d x}=1+y \sin x$ where $\left(-\frac{\pi}{2}<x<\frac{\pi}{2}\right) .$Mathematicshttps://mathsgee.com/35656/integrating-factor-linear-differential-equation-where-rightThu, 13 Jan 2022 03:19:11 +0000