# Recent questions tagged plane

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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.
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.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 ...
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Find the inverse to a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).
Find the inverse to a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).Find the inverse to a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise). ...
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Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.
Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed. ...
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Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees.
Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees.Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees. ...
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Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis. ...
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Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise).Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees $(+45$ degrees means 45 degrees counterclockwise). ...
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Determine $\frac{\mathrm{d} y}{\mathrm{~d} x}$ if $y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}$
Determine $\frac{\mathrm{d} y}{\mathrm{~d} x}$ if $y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}$Determine $\frac{\mathrm{d} y}{\mathrm{~d} x}$ if \ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \ ...
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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 $R^3$?How do I determine the equation of a normal in $R^2$ or $R^3$? ...
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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 $R^{3} ?$
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 $R^{3} ?$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 $R^{3} ?$ ...
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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
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ isProve 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| ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. 1 answer 55 views Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1.Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. 0 answers 156 views Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a 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. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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? 0 answers 50 views 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?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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to 0 answers 58 views The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal toThe distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to &nbsp; A) \dfrac{1}{3} B) 3 C) \dfrac{1}{15} D) 5 E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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. 0 answers 155 views 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.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. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the equation of the plane that contains the z-axis and the point (3,1,2). 0 answers 187 views Find the equation of the plane that contains the z-axis and the point (3,1,2).Find the equation of the plane that contains the z-axis and the point (3,1,2). ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the equation of the plane through the points (3,-2,5),(1,4,-1),(2,-6,7) ? 0 answers 65 views Which of the following is the equation of the plane through the points (3,-2,5),(1,4,-1),(2,-6,7) ?Which of the following is the equation of the plane through the points (3,-2,5),(1,4,-1),(2,-6,7) ? \text { A. }\left|\begin{array} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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} 0 answers 149 views 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}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 \m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the unit vector in direction of a \times b if a=(2,1,1) and b=(-1,2,2) ? 0 answers 50 views Which of the following is the unit vector in direction of a \times b if a=(2,1,1) and b=(-1,2,2) ?Which of the following is the unit vector in direction of a \times b if a=(2,1,1) and b=(-1,2,2) ? &nbsp; A. \left(-\frac{1}{2}, \frac{1}{2}, ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (-1,1,1) to the plane 0 answers 41 views The distance from the point (-1,1,1) to the planeThe distance from the point (-1,1,1) to the plane$$ 2 x-10 y+11 z-4=0 $$is equal to &nbsp; A) 3 B) \frac{1}{3} C) 5 D) \frac{1}{5} E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write the equation of the plane through the points  (3,-2,5),(1,4,-1),(2,-6,7)  0 answers 38 views Write the equation of the plane through the points  (3,-2,5),(1,4,-1),(2,-6,7) Write the equation of the plane through the points$$ (3,-2,5),(1,4,-1),(2,-6,7)  ...
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Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.
Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.Consider the differential equation $\frac{d x}{d y}=\frac{y^{2}+y^{2} e^{\left(\frac{x}{y}\right)^{2}}+2 x^{2} e^{\left(\frac{x}{y}\right)^{2}}}{2 x y ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the particular solution of the differential equation given that$y=1$when$x=0$. 0 answers 44 views Find the particular solution of the differential equation given that$y=1$when$x=0$.Find the particular solution of the differential equation given that$y=1$when$x=0$. &nbsp; NB:$\dfrac{d x}{d y}=\dfrac{y^{2}+y^{2} e^{\left(\fra ...
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The 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
The 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 $y=1$ isThe 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 ...
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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 $\left(-\frac{\pi}{2}<x<\frac{\pi}{2}\right) .$
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 $\left(-\frac{\pi}{2}<x<\frac{\pi}{2}\right) .$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 $\left(-\frac{\pi}{2}&lt;x& ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve$\cos x \frac{d y}{d x}=1+y \sin x$(where$\left.-\frac{\pi}{2}<x<\frac{\pi}{2}\right)$explicitly. 0 answers 109 views Solve$\cos x \frac{d y}{d x}=1+y \sin x$(where$\left.-\frac{\pi}{2}<x<\frac{\pi}{2}\right)$explicitly.Solve &nbsp;$\cos x \frac{d y}{d x}=1+y \sin x$where$ \left(-\frac{\pi}{2}&lt;x&lt;\frac{\pi}{2} \right) $explicitly. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A partial fraction decomposition of$\frac{x^{3}+3 x^{2}+4}{x\left(x^{2}+1\right)^{2}(x-1)}$is of the form 0 answers 87 views A partial fraction decomposition of$\frac{x^{3}+3 x^{2}+4}{x\left(x^{2}+1\right)^{2}(x-1)}$is of the formA partial fraction decomposition of$\frac{x^{3}+3 x^{2}+4}{x\left(x^{2}+1\right)^{2}(x-1)}$is of the form A.$\quad \frac{A}{x^{2}+1}+\frac{B}{\lef ...
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Find the general explicit solution of the differential equation $y^{\prime}=\left(x^{2}+3\right)\left(y^{2}+1\right)$.
Find the general explicit solution of the differential equation $y^{\prime}=\left(x^{2}+3\right)\left(y^{2}+1\right)$.Find the general explicit solution of the differential equation $y^{\prime}=\left(x^{2}+3\right)\left(y^{2}+1\right)$. ...
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Find the particular solution of the differential equation $y^{\prime}=\left(x^{2}+4\right)\left(y^{2}+1\right)$ which satisfices the initial condition $y(0)=1$.
Find the particular solution of the differential equation $y^{\prime}=\left(x^{2}+4\right)\left(y^{2}+1\right)$ which satisfices the initial condition $y(0)=1$.Find the particular solution of the differential equation $y^{\prime}=\left(x^{2}+4\right)\left(y^{2}+1\right)$ which satifies the initial condition $... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the particular solution to$y(x+1)+y^{\prime}=0$that satisfies$y(-2)=1 ?$1 answer 41 views What is the particular solution to$y(x+1)+y^{\prime}=0$that satisfies$y(-2)=1 ?$What is the particular solution to$y(x+1)+y^{\prime}=0$that satisfies$y(-2)=1 ?$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How do you solve the differential equation$\frac{d y}{d x}=6 y^{2} x$, where$y(1)=\frac{1}{25}$? 1 answer 110 views How do you solve the differential equation$\frac{d y}{d x}=6 y^{2} x$, where$y(1)=\frac{1}{25}$?How do you solve the differential equation$\frac{d y}{d x}=6 y^{2} x$, where$y(1)=\frac{1}{25}$? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Is $3-x^{-1}$ a polynomial? 1 answer 46 views Is $3-x^{-1}$ a polynomial?Is $3-x^{-1}$ a polynomial? ... close 0 answers 43 views If two lines in the cartesian plane are perpendicular, show that the angles they make with the positive $x$ axis can be written as $\alpha$ and $\frac{\pi}{2}+\alpha$ for some $\alpha$.If two lines in the cartesian plane are perpendicular, show that the angles they make with the positive $x$ axis can be written as $\alpha$ and $... close 0 answers 100 views The U.S. federal debt at the end of 2001 was \(\ 5.77$ trillion, and grew to $\ 6.20$ trillion by the end of 2002 . At the end of 2005 it was $\ 7.91$ trillion, and grew to $\ 8.45$ trillion by the end of $2006^{3}$.The U.S. federal debt at the end of 2001 was $\ 5.77$ trillion, and grew to $\ 6.20$ trillion by the end of 2002 . At the end of 2005 it was $\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A virtual image can be formed by one or more of the following single mirrors? Identify them. 1 answer 116 views A virtual image can be formed by one or more of the following single mirrors? Identify them.A virtual image can be formed by one or more of the following single mirrors? Identify them. w) plane mirror x) concave spherical mirror y) convex ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How can we solve the equation \((4 z-4)^{2}-6=58$ ? 1 answer 73 views How can we solve the equation $(4 z-4)^{2}-6=58$ ?How can we solve the equation $(4 z-4)^{2}-6=58$ ? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find an equation of the line having slope $-3$ and containing $(3,-1)$. 1 answer 65 views Find an equation of the line having slope $-3$ and containing $(3,-1)$.Find an equation of the line having slope $-3$ and containing $(3,-1)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$. 1 answer 84 views Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$.Determine the equation of the circle with centre $(-2 ;-1)$ through the point $(5 ; 1)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$. 1 answer 151 views Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$.Determine the equation of the circle with centre $(-3 ; 3)$ through the point $(5 ; 1)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$. 1 answer 182 views Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$.Determine the equation of the circle with centre $(5 ;-3)$ through the point $(3 ; 2)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If $y=\log _{a} x$ passes through $(9 ;-2)$, determine the value of $a$. 1 answer 95 views If $y=\log _{a} x$ passes through $(9 ;-2)$, determine the value of $a$.If $y=\log _{a} x$ passes through $(9 ;-2)$, determine the value of $a$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If $y=\log _{5} x$, calculate the $x$-intercept. 1 answer 68 views If $y=\log _{5} x$, calculate the $x$-intercept.If $y=\log _{5} x$, calculate the $x$-intercept. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If $y=\log _{a} x$ passes through $(5 ; 1)$, determine the value of $a$. 1 answer 95 views If $y=\log _{a} x$ passes through $(5 ; 1)$, determine the value of $a$.If $y=\log _{a} x$ passes through $(5 ; 1)$, determine the value of $a$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the remainder by using the remainder theorem.$f(c)=3 c^{3}-6 c^{2}+3 c-4 ; g(c)=c+6$1 answer 92 views Determine the remainder by using the remainder theorem.$f(c)=3 c^{3}-6 c^{2}+3 c-4 ; g(c)=c+6$Determine the remainder by using the remainder theorem.$f(c)=3 c^{3}-6 c^{2}+3 c-4 ; g(c)=c+6$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the remainder by using the remainder theorem.$f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$1 answer 78 views Determine the remainder by using the remainder theorem.$f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$Determine the remainder by using the remainder theorem.$f(r)=-5 r^{3}+8 r^{2}-4 r-7 ; g(r)=r+3$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the arithmetic mean of 16 and$-2 .$1 answer 57 views Determine the arithmetic mean of 16 and$-2 .$Determine the arithmetic mean of 16 and$-2 .$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the slope of the line going through$(-3,2)$and$(-4,2)$1 answer 70 views Find the slope of the line going through$(-3,2)$and$(-4,2)$Find the slope of the line going through$(-3,2)$and$(-4,2)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the other name for Brewster's angle? 1 answer 67 views What is the other name for Brewster's angle?What is the other name for Brewster's angle? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Suppose the position of an object at time$t$is given by$f(t)=-49 t^{2} / 10+5 t+10 .$Find a function giving the speed of the object at time$t .$1 answer 272 views Suppose the position of an object at time$t$is given by$f(t)=-49 t^{2} / 10+5 t+10 .$Find a function giving the speed of the object at time$t .$Suppose the position of an object at time$t$is given by$f(t)=-49 t^{2} / 10+5 t+10 .$Find a function giving the speed of the object at time$t .$... close 1 answer 223 views Find the parametric representation of the line$L$in$\mathbf{R}^{4}$passing through the point$P(1,2,3,-4)$and in the direction of$u=[5,6,-7,8]$. Also, find the point$Q$on$L$when$t=1$.Find the parametric representation of the line$L$in$\mathbf{R}^{4}$passing through the point$P(1,2,3,-4)$and in the direction of$u=5,6,-7,8\$. ...