Thread: vector

The diagram shows non-collinear points O , A , B with P on the line OA such that OP:PA=2:1 and Q on the line AB such that AQ:QB=2:3 . The lines PQ and OB produced meet at the point R . If and

(1) Show that

I managed to prove this .

(2) Find the position vector of R , relative to O , in terms of b

need help on this .

Hello hooke

Originally Posted by hooke

The diagram shows non-collinear points O , A , B with P on the line OA such that OP:PA=2:1 and Q on the line AB such that AQ:QB=2:3 . The lines PQ and OB produced meet at the point R . If and

(1) Show that

I managed to prove this .

(2) Find the position vector of R , relative to O , in terms of b

need help on this .

The key to this is to realise that (i) is a multiple of and (ii) is a multiple of , since the points are collinear and are collinear. So, suppose:

and

Therefore:

and

But:

Now the coefficient of on the LHS is zero. Therefore:

And if we now compare coefficients of , we get:

Hence:

Grandad