1. The position vectors of the non-collinear points A, B, C are a, b, c respectively....

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1. The position vectors of the non-collinear points A, B, C are a, b, c respectively. E lies on BC with BE|/|EC| = 2/3, F lies on Ca with CF/|FA| = 1/4, and G lies %3D 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. O and Rare collinear and that PO = LOR. 1. The position vectors of the non-collinear points A, B, C are a, b, c respectively. E lies on BC with BE|/|EC| = 2/3, F lies on Ca with CF/|FA| = 1/4, and G lies %3D 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. O and Rare collinear and that PO = LOR.