WAEC Further Mathematics 2014 Theory question 105

Theory question 105

Vectors

The position vectors of points P, Q and R are 11i + j, 5i + (13/3)j and 2i + 6j respectively. (a) Show that P, Q and R lie on a straight line. (b) Find the ratio |PQ| : |QR|.

Show the model answer

Model answer

(a) PQ = (−6, 10/3), QR = (−3, 5/3).
PQ = 2QR, so PQ and QR are parallel with Q in common: P, Q, R are collinear.
(b) |PQ| = 2√106/3, |QR| = √106/3, so |PQ| : |QR| = 2 : 1.

Explanation

Collinear points: one connecting vector is a multiple of the other.