# Recent questions tagged line

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Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$.
Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$.Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$. (a) Find the midpoint of the line segment connecting the points $P$ and $Q$. (b) Find th ...
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Let $P$ be the point $(1,3,7)$. If the point $(4,0,-6)$ is the midpoint of the line segment connecting $P$ and $Q$, what is $Q$ ?
Let $P$ be the point $(1,3,7)$. If the point $(4,0,-6)$ is the midpoint of the line segment connecting $P$ and $Q$, what is $Q$ ?Let $P$ be the point $(1,3,7)$. If the point $(4,0,-6)$ is the midpoint of the line segment connecting $P$ and $Q$, what is $Q$ ? ...
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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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Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars.
Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars.Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars. a) (Pythagoras) Show that $\|Z\|^{2}=a^{2}\|U\|^{2}+b ... close 0 answers 8 views Let \(A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and $A \vec{w}$ are orthogonal.Let $A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and ...
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Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$.Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \v ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Think of the matrix \(A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ as mapping one plane to another.
Think of the matrix $A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ as mapping one plane to another.Think of the matrix $A=\left(\begin{array}{ll}a &amp; b \\ c &amp; d\end{array}\right)$ as mapping one plane to another. a) If two lines in the firs ...
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Let $U$ and $V$ both be two-dimensional subspaces of $\mathbb{R}^{5}$, and let $W=U \cap V$. Find all possible values for the dimension of $W$.
Let $U$ and $V$ both be two-dimensional subspaces of $\mathbb{R}^{5}$, and let $W=U \cap V$. Find all possible values for the dimension of $W$.Let $U$ and $V$ both be two-dimensional subspaces of $\mathbb{R}^{5}$, and let $W=U \cap V$. Find all possible values for the dimension of \(W ...
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Interactive video: Elements of Art - Line
Interactive video: Elements of Art - Line Interactive video: Elements of Art - Line&nbsp; &nbsp; &nbsp; ...
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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 $$D=\frac{\left| ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. 1 answer 11 views Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1.Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. 0 answers 8 views Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain.Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do? 0 answers 5 views A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do?A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$0 answers 10 views Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to 0 answers 7 views The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal toThe distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to &nbsp; A) \dfrac{1}{3} B) 3 C) \dfrac{1}{15} D) 5 E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection. 0 answers 7 views Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection.Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the distance D between the point P_{0}\left(x_{0}, y_{0}\right) and the line a x+b y+c=0 in R^2? 1 answer 10 views What is the distance D between the point P_{0}\left(x_{0}, y_{0}\right) and the line a x+b y+c=0 in R^2?What is the distance D between the point P_{0}\left(x_{0}, y_{0}\right) and the line a x+b y+c=0 in R^2? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right. $$0 answers 11 views Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right. $$Which of the following is the direction vector of the line$$ \left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right.  &nbsp; ...
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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} ...
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false?
Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false?Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false? A. $-a \time ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$a, b$and$c$be vectors in$\mathrm{R}^{3}$, such that$a \cdot(b \times c)=0$. Then 0 answers 12 views Let$a, b$and$c$be vectors in$\mathrm{R}^{3}$, such that$a \cdot(b \times c)=0$. ThenLet$a, b$and$c$be vectors in$\mathrm{R}^{3}$, such that$a \cdot(b \times c)=0$. Then A.$a, b$and$c$are colinear B.$a, b$and$c$lie on t ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the equation of the plane which passes through the point$A(-3,4,-3)$and contains the line$v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$0 answers 9 views Which of the following is the equation of the plane which passes through the point$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 ...
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 $b=(-1,2,2) ?$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}, ...