Question

Abcd is a parallelogram show that 2dc vector minus bd vector equal to ac vector

Answer 1

let AB = a = DC

BC = b = AD

AC, DB be the diagonals {a,b are vectors}

AC+DB

(AB+BC)+ (DA+DC)

(a+b)+ (-b+a) {-b as the direction is negative}

2a

=2DC

Hence, 2DC=AC+DB

2DC-DB = AC