`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

Take A as origin.

Let `vec{a}, vec{b}` be the position vectors of the points `B, D` respectively.

Then, `vec{A B}=vec{a}` and `vec{A D}=vec{b}`

By parallelogram law of addition of vectors,


`vec{AC}=vec{AB}+vec{AD} `

`Rightarrow vec{AC}=vec{a}+vec{b}`

`therefore` The position vector of `C` is `vec{a}+vec{b}`.

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