Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:2, 3:7 respectively. Prove thatAL + BM + CŃ is a vector parallel to CK where K divides AB in the ratio 1: 3.

Explanation

Let `\vec{a}, \vec{b}` and `\vec{c}` be position `N^{3} A` of vertices `A, B` and `C`.


`P \cdot V` of `C=\frac{\vec{c}+4 \vec{b}}{5}`


`M=\frac{3 \vec{a}+2 \vec{c}}{5}`


`N=\frac{3 \vec{b}+7 \vec{a}}{10} \quad(P V arrow Position )`


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