With respect to an origin O, the points A and B have position vectors a and b respectively. The point L lies on the line segment AB such that AL = 1/2 LB and the point M lies on OL produced such that OM = 6OL.
(i) Find the position vectors OL and OM, giving your answers in terms of a and b.
(ii) Show that the vector equation of the line BM can be written as r = 4Xa + (1 + X) b, where X is a parameter. Find in a similar form the vector equation of the line OA in terms of a parameter Y.
(iii) Find, in terms of a, the position vector of the point P where the lines BM and OA meet
(iv) it is given that a and b are unit vectors such that a and b are perpendicular. By using scalar product, find |PM|^2
I am unable to solve (iii) where the answer is OP = -4a. I am unsure of the steps to reach the answer.