Chapter 9.5, Problem 37E

To determine

(a)

To find:

The triple products $u\cdot \left(v\times w\right)$, $u\cdot \left(w\times v\right)$, $v\cdot \left(u\times w\right)$, $v\cdot \left(w\times u\right)$, $w\cdot \left(u\times v\right)$, $w\cdot \left(v\times u\right)$.

To determine

(b)

To find:

The relationship among these six triple products.

To determine

(c)

To prove:

The conjecture made in part (b).