The position vector of the point which divides the join of points `2veca-3vecbandveca+vecb` in the ratio 3:1, is

Options

A. `(3veca-2vecb)/(2)`
B. `(7veca-8vecb)/(7)`
C. `(3veca)/(4)`
D. `(5veca)/(4)`

Answer

D

Explanation

Let the position vector of the point R divides the join of points `2veca-3vecbandveca+vecb`.
:.Position vector `R=(3(veca+vecb)+1(2veca-3vecb))/(3+1)`
Since, the position vector of a point R dividing the line segment joining the points P and Q, whose position vectors are `vecpandvecq` in the ratio m:n internally, is given by `(mvecq+nvec p)/(m+n)`
`:.R=(5veca)/(4)`