Relative to a fixed origin, *O*, the points *A *and *B *have position vectors

(1i, 5j, 1k)

and

(6i, 3j, 6k)

respectively.

Find, in exact, simplified form,

*(i) *

the cosine of angle *AOB*, [4] *(ii) *

the area of triangle *OAB*, [3]

*(iii) *the shortest distance from *A *to the line *OB*. [2]

I successfully found the answer to part (i) to be $\displaystyle \frac{\sqrt{3}}{3}$.

I have the mark scheme and the answer to part (ii) is $\displaystyle \frac{27}{2}\sqrt{2}$

and the answer to part (iii) is $\displaystyle 3\sqrt{2}$

Please explain to me how to do parts (ii) and (iii)

Thanks