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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.4.4 .
Suppose
\(\vu = \langle 3, 5, -1\rangle\) and
\(\vv = \langle 2, -2, 1\rangle\text{.}\)
(a) Find two unit vectors orthogonal to both
\(\vu\) and
\(\vv\text{.}\)
(b) Find the volume of the parallelepiped formed by the vectors
\(\vu\text{,}\) \(\vv\text{,}\) and
\(\vw = \langle 3,3,1\rangle\text{.}\)
(c) Find a vector orthogonal to the parallelogram containing the points
\((0,1,2)\text{,}\) \((4,1,0)\text{,}\) and
\((-2,2,2)\text{.}\)
(d) Given the vectors
\(\vu\) and
\(\vv\) shown below in
Figure 9.4.10 , sketch the cross products
\(\vu\times\vv\) and
\(\vv\times\vu\text{.}\)
Figure 9.4.10. Vectors \(\vu\) and \(\vv\)
(e) Are the vectors
\(\va = \langle 1,3,-2\rangle\text{,}\) \(\vb=\langle2,1,-4\rangle\text{,}\) and
\(\vc=\langle 0, 1, 0\rangle\) in standard position coplanar? Use the concepts from this section to explain your answer.
