Relative to a fixed origin,O, the pointsAandBhave position vectors

(1i, 5j, 1k)

and

(6i, 3j, 6k)

respectively.

Find, in exact, simplified form,

(i)

the cosine of angleAOB, [4]

(ii)

the area of triangleOAB, [3]

(iii)the shortest distance fromAto the lineOB. [2]

I successfully found the answer to part (i) to be .

I have the mark scheme and the answer to part (ii) is

and the answer to part (iii) is

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

Thanks