# Recent questions tagged plane

Find all linear maps $L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ whose kernel is exactly the plane $\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathbb{R}^{3} \mid\right.$ $\left.x_{1}+2 x_{2}-x_{3}=0\right\}$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 ... close 0 answers 2 views 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, 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 t ...
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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): 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{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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.
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.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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 $A^{5}=I$.Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$. ...
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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.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 leav ...
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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| ...
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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 $2 x-3 y+6 z=-1$.Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$. ...
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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.Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain. ...
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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?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 ...
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The distance from the point $(1,1,1)$ to the plane $2 x-10 y+11 z-4=0$ is equal to
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 ...
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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.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. ...
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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 $(3,1,2)$.Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$. ...
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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 $(3,-2,5),(1,4,-1),(2,-6,7) ?$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} ...
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 $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$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) ?$0 answers 4 views Which of the following is the unit vector in direction of$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}, ...