M and N are the mid points of the sides BC and CD of a parallelogram ABCD respectively then A M + A N =

Step-by-step solution

Let position vectors of A, B, C, D are 0 , b , c , d respectively. aligned & A C = c & B C = c - b aligned M is mid point of BC aligned & B M = 1 2 B C = 1 2 ( c - b ) & A M = A B + B M aligned = b + 1 2 ( c - b )= 1 2 ( b + c ) aligned & A D = d & D C = c - d aligned N is mid point of DC D N = 1 2 ( c - d ) aligned & A N = A D + D N = d + 1 2 ( c - d )= 1 2 ( c + d ) & A M + A N = 1 2 ( b + c )+ 1 2 ( c + d ) aligned = c + 1 2 ( b + d ) ABCD is parallelogram b + d = c A M + A N = c + 1 2 c = 3 2 c = 3 2 A C