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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 9.4.2 .
Suppose
\(\vu = \langle 0, 1, 3\rangle\) and
\(\vv = \langle 2, -1, 0\rangle\text{.}\) Use equation
(9.4.1) for the following.
(a) Find the cross product
\(\vu\times\vv\text{.}\)
(b) Evaluate the dot products
\(\vu\cdot(\vu\times\vv)\) and
\(\vv\cdot(\vu\times\vv)\text{.}\) What does this tell you about the geometric relationship among
\(\vu\text{,}\) \(\vv\text{,}\) and
\(\vu\times\vv\text{?}\)
(c) Find the cross product
\(\vv\times \vi\text{.}\)
(d) Recall that multiplication of real numbers is
associative . For example,
\((2\cdot 5)\cdot 3 = 2\cdot(5\cdot 3)\text{.}\) Is it true that the cross product of vectors is associative? For instance, is it true that
\((\vu\times\vv)\times\vi = \vu\times(\vv\times\vi)\text{?}\)
(e) Find the cross product
\(\vu\times\vu\) and write a sentence or two to explain the meaning of your result.
