`veca` and `vecb` are the position vectors of A,B respectively and C is a point on AB produced such that AC=3 AB. Then the position vector of C is

Options

A. `3 vec(a)-2 vec(b)`
B. `3vec(b)-2vec(a)`
C. `3vec(a)+2 vec(a)`
D. `2vec(a)-3vec(b)`

Answer

B

Explanation

Let the position vector for C be `vec(c )`
Clearly, B divides AC internally in the ratio `1:2`.
`therefore vec(b)=(2vec(a)+1*vec(c))/(2+1)rArr vec(c) = 3 vec(b) - 2 vec(a) `