The straight line l has the following vector equation: r = -2 i - 12 j - 9 k + ( I + 3 j

The straight line l has the following vector equation: r = -2 i  - 12 j  - 9 k  + λ( I  + 3 j  + 2 k ),

Where λ is a scalar parameter.

The point P(a, b, 3) lies on l ,

(i) Find the value of each of the scalar constants a and b.

The point O represents a fixed origin,

The point Q lies on l , so that OQ is perpendicular to  l .

(ii) Show that the coordinates of Q are (2,0,-1). 

(iii) Find the exact area of the triangle OPQ.