If in parallelogram ABCD, diagonal vectors are ` vec A C=2 hat i+3 hat j+4 hat k` and ` vec B D=-6 hat i+7 hat j-2 hat k ,` then find the adjacent side vectors ` vec A B` and ` vec A D`

Explanation

Let `vec(AB) =veca and vec(AD)=vecb`. Then
`" "vec(AC)=veca+vecb and vec(BD)=vecb-veca`
`rArr" "vecb=(vec(AC)+vec(BD))/(2) and veca=(vec(AC)-vec(BD))/(2)`
`rArr" "vec(AB)=-2hati+35 +hatk and vec(AD)=4hati-2hatj+3hatk`