1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. a + 2b, a+b and Aa +b, find the value of A if P, Q and R lie on a straight line. 2 4 2. ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA re- spectively and are such that AQ = CP= 2units. If the point R lies on AB produced so that BR = lunit, prove that P, Q. R are collinear. 3. Prove that the points with position vectors a + 2b, 2a b and 3a- 4b are collinear. 4. The position vectors of the non-collinear points A, B, C are a, b, e respectively. E lies on BC with |BE|/ EC| = 2/3, F lies on Ca with |CF/|FA| = 1/4, and G lies on AB produced with GB/GA| = 1/6. Determine the position vectors of E, F, G in terms of a, b, c and deduce that E, F.G lie on a straight line. 5. E and F are points of the sides AD, BC of a quadrilateral ABCD such that AE = kED and BF kFC. If P, Q, R are the midpoints of AB, EF, DC respectively, show that P, Q and R are collinear and that PQ = kQR. %3D