Let $\displaystyle \mathbf{a,b,c}$ be three vectors in $\displaystyle \mathbb{R}^3$ which satisfy the relations $\displaystyle \mathbf{b=c \times a}\ and\ \mathbf{c=a \times b}$

1) Show that $\displaystyle \mathbf{a, b\ and\ c}$ are a set of mutually orthogonal vectors

2) Show that $\displaystyle \mathbf{b\ and\ c}$ are of equal length and that if $\displaystyle \mathbf{b \neq 0}$, then $\displaystyle \mathbf{a}$ is a unit vector.