Question

A D O D B ABCD is a parallelogram. The diagonals of the parallelogram intersect at O. DO= a and CÓ = b a) Find, in terms of b, the vector CA. b) Find, in terms of a and b, the vector DC. c) Find, in terms of a and b, the vector CB. O (1) (1) (1) To​

Answer 1

In a parallelogram where diagonals intersect at O and DO = a, CO = b: CA = 2a, DC = a - b, and CB = 0.

a) Finding vector CA:

In a parallelogram, the diagonals bisect each other. Therefore, CO = OA = a.

Vector CA can be expressed as the sum of vectors CO and OA:

CA = CO + OA = a + a = 2a

b) Finding vector DC:

Vector DC is the difference between vectors CO and DO:

DC = CO - DO = a - b

c) Finding vector CB:

Vector CB can be expressed as the sum of vectors CO and BO:

CB = CO + BO = a - a = 0