2. OA = aOB = bAC = 2aOD = 3b Prove that AB is parallel to CD. (VECTORS, PROOF) 2a2a 2b2b Prove parallel

3. CDEF is a quadrilateral with CD = a, DE = b and FC = a - b. (a) Express CE,FE and FM in terms of a and b. X is the point on such that FX : XM = 4 : 1. (b) Prove that C, X and E lie on the same straight line. CE = ?, FE = ?, FM = ? PROVE CXE is straight line (VECTORS, PROOF) FX : XM = 4 : 1 CE = a + b FE = (a – b) + a + b = 2a FM = (a – b) + a + ½b = 2a - ½b CX = -(a – b) + ⅘( 2a - ½b) = ⅗ a + ⅗ b CX = ⅗ CE therefore CXE is straight line.