Chapter 2.3, Problem 52E

To determine

a)

To verify:

For $u=\left[\begin{array}{l}{u}_1\\ u_2\\ u_3\end{array}\right]$ and $v=\left[\begin{array}{l}{v}_1\\ v_2\\ v_3\end{array}\right]$ verify that ${\left|\left|u\times v\right|\right|}^2={\left|\left|u\right|\right|}^2{\left|\left|v\right|\right|}^2-{\left(u\cdot v\right)}^2$.

To determine

b)

To show:

Show that $\left|\left|u\times v\right|\right|=\left|\left|u\right|\right|\left|\left|v\right|\right|\sin \theta$, where $\theta$ is the angle between $u$ and $v$.