# Recent questions tagged plane

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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?
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?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? (a) The ob ...
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If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.
If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain. ...
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In $\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$.
In $\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$.In $\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$. ...
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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.In $\mathbb{R}^{3}$, let $N$ be a non-zero vector and $X_{0}$ and $Z$ points. a) Find the equation of the plane through the origin that is ort ...
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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?
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?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 $\|V+W\| ?$ Whe ...
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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 9 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 ...
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 ...