# Math Help - Vectors question

1. ## Vectors question

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 $\frac{\sqrt{3}}{3}$.

I have the mark scheme and the answer to part (ii) is $\frac{27}{2}\sqrt{2}$
and the answer to part (iii) is $3\sqrt{2}$

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

2. Find the length AB, OA and OB
Then Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2, a, b and c are the sides of the triangle AOB.

If the shortest distance from
A to the line OB. is d, then

Area AOB = 1/2*d*OB.

Find OB. You have already calculated area AOB. Find d.