Activity 9.5.2

Suppose $\vu = \langle 0, 1, 3\rangle$ and $\vv = \langle 2, -1, 0\rangle$. Use equation this equation for the following.

1. Find the cross product $\vu\times\vv$.

2. Evaluate the dot products $\vu\cdot(\vu\times\vv)$ and $\vv\cdot(\vu\times\vv)$. What does this tell you about the geometric relationship among $\vu$, $\vv$, and $\vu\times\vv$?

3. Find the cross product $\vv\times \vi$.

4. Recall that multiplication of real numbers is associative. For example, $(2\cdot 5)\cdot 3 = 2\cdot(5\cdot 3)$. Is it true that the cross product of vectors is associative? For instance, is it true that $(\vu\times\vv)\times\vi = \vu\times(\vv\times\vi)$?

5. Find the cross product $\vu\times\vu$ and write a sentence or two to explain the meaning of your result.