Let $\displaystyle \vec{a}$ and $\displaystyle \vec{a}$ be 3d vectors.

Explain in words with the aid of a diagram why:

($\displaystyle \vec{a}$x$\displaystyle \vec{b}$).$\displaystyle \vec{b}$ = 0.

Explain with the aid of a diagram, that if

$\displaystyle \vec{b}$x($\displaystyle \vec{a}$.$\displaystyle \vec{b}$) = $\displaystyle \vec{a}$,

what is $\displaystyle \vec{a}$.$\displaystyle \vec{b}$?

should be using right hand rules etc