If you start at the initial point \((3,7,1)\)
and travel to the terminal point \((1,2,5),\)
along what vector did you travel?
Let \(A\) be the point \((2,-9,1)\)
and let \(B\) be the point \((3,2,-4)\)
What are the components of the vector \(\overrightarrow{AB}?\)
What are the components of the vector \(\overrightarrow{BA}?\)
If you start at the initial point \((-2,7,6)\)
and travel along a vector \(\langle -1,3,0 \rangle,\)
what are the coordinates of the terminal point?
Given points \(A\) and \(B\)
such that the coordinates of \(A\) are \((0,-3,1)\)
and such that \(\overrightarrow{AB} = \bigl\langle 10,2,-5 \bigr\rangle\)
what must the coordinates of \(B\) be?
Let \(\bm{v} = \langle 3,2,-4 \rangle.\)
What is the magnitude of \(\bm{v}?\)
What is \(\bm{\hat{v}},\) the unit vector in the direction of \(\bm{v}?\)
What angle does \(\bm{v} = \langle 3,0,2 \rangle\)
make with the \(z\)-axis?
What angle does \(\bm{u} = \langle 1,3,-2 \rangle\)
make with the \(xy\)-plane?
Sketch the vectors \(\bm{u} = \langle 3,-3,5 \rangle\)
and \(\bm{v} = \langle 2,5,-4 \rangle\) in \(xyz\)-space,
then explicitly calculate each of the following:
\( \bm{u} + \bm{v} \)
\( \bm{u} - \bm{v} \)
\( |\bm{u}| \)
\( |\bm{v}| \)
\( \bm{\hat{u}} \)
\( \bm{\hat{v}} \)
\( 3\bm{u} \)
\( \bm{u}\cdot\bm{v} \)
\( \bm{u} - 2\bm{v} \)
\( \bm{v} + \langle 1,-2,3 \rangle \)
\( \bm{u} + 2\mathbf{j}-\mathbf{k} \)
What are the three acute angles that \(\bm{u}\) makes with the coordinate axes?
What are the three acute angles that \(\bm{v}\) makes with the coordinate axes?
What is the measure of the angle between the vectors \(\bm{u}\) and \(\bm{v}?\)
What is the area of the triangle framed by \(\bm{u}\) and \(\bm{v}?\)
What is the measure of angle between
\(\bm{u} = \langle 7,-2,1\rangle\)
and \(\bm{v} = \langle 3,5,-3 \rangle?\)
What is the area of the triangle framed by those vectors?
What is the area of the triangle in space
with vertices located at the coordinates
\((1,1,1)\) and \((3,-3,8)\) and \((2,7,0)?\)