Chapter 13.4, Problem 57E

(a)

To determine

Whether the statement “The cross product of two non-zero vectors is a nonzero vector.” is true and give proper explanation or counterexample.

(b)

To determine

Whether the statement “ $\left|u\times v\right|$ is less than both $\left|u\right|$ and $\left|v\right|$” is true and give proper explanation or counterexample.

(c)

To determine

Whether the statement “If u points east and v points south, then $u\times v$ points west.” is true and give proper explanation or counterexample.

(d)

To determine

Whether the statement “If $u\times v=0$ and $u\cdot v=0$, then either $u=0$ or $v=0$.” is true and give proper explanation or counterexample.

(e)

To determine

Whether the statement “Law of cancellation? If $u\times v=u\times w$,

then $v=w$.” is true and give proper explanation or counterexample.