L and M are two points with position vectors `2vec(a)-vec(b)andvec(a)+2vec(b)`, respectively. The position vector of the pont N which divides the line segment LM in the ratio 2:1 externally is

Options

A. `3vec(b)`
B. `4vec(b)`
C. `5vec(b)`
D. `3vec(a)+4vec(b)`

Answer

C

Explanation

Given,
`L=2vec(a)-vec(b)`
and `M=vec(a)+2vec(b)`
Since , N divides LM in the ratio 2:1 externally.
`:.` Position vector of N
`=(2(vec(a)+2vec(b))-1(2vec(a)-vec(b)))/(2-1)`
`=(2vec(a)+4vec(b)-2vec(a)+vec(b))/(1)=5vec(b)`