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?
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?
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 is the angle between the vectors \(\bm{u}\) and \(\bm{v}?\)
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?