`A B C D` is a parallelogram. If `La n dM` are the mid-points of `B Ca n dD C` respectively, then express ` vec A La n d vec A M` in terms of ` vec A Ba n d vec A D` . Also, prove that ` vec A L+ vec A M=3/2 vec A Cdot`

Explanation

`vec(AL) = vec(AB) + vec(BL) = vec(AB) + (1)/(2) vec(BC) `
`" " = vec(AB) + (1)/(2) vec(AD)`
`vec(AM) = vec(AD) + vec(DM) = vec(AD) + (1)/(2) vec(DC)`
`" " = vec(AD) + (1)/(2) vec(AB)`
Adding. `vec(AL) + vec(AM) + (3)/(2) (vec(AB) + vec(AD))`
`" " =(3)/(2)(vec(AB) + vec(BC)) = (3)/(2) vec(AC)`