`ABCD` is a parallelogram Fig. 2 (c ) .64. AC` and (BD) are its diagonals. Show that
` (a) vec (AC) +vec (BD) =2 vec (BC)`
(b) `vec (AC) - vec (BD) =2 vec (AB)`
.

Explanation

(a) Refer to Fig. 2 (c ). 64, using trianle law of v ec tors, we have,
` vec (AC) + vec (BD) =(vec (AB) + vec (BC) + vec (BC) + vec (CD)`
`=vec (AB) + 2 vec (BC) + vec (CD)`
` =vec (AB) = 2 vec (BC)-vec (AB)`
` (:. Vec (CD) =- vec (AB)`
or ` vec (AC) + vec (BD) =2 vec (BC)`
(b) ` vec(AC)- vec (BD) =vec(AB) + vec (BC) -vec (BC) + vec AB)`
`= vec (AB) -vec (CD)`
` vec (AC) -vec (BC) =(AB) -(-AB) =2 VEC (AB)`.