Let `A(1,-1,2) and B(2,3-1)` be two points. If a point P divides AB internally in the ratio `2:3`, then the position vector of P is

Options

A. `(1)/(sqrt(5))(hat(i)+hat(j)+hat(k))`
B. `(1)/(sqrt(3))(hat(i)+6hat(j)+hat(k))`
C. `(1)/(sqrt(3))(hat(i)+hat(j)+hat(k))`
D. `(1)/(5)(7hat(i)+3hat(j)+4hat(k))`

Answer

D

Explanation

`alpha=(2.2+3.1)/(2+3)=(7)/(5)`
`beta=(2.3+3.(-1))/(2+3)=(3)/(5)`

and `gamma =(2(-1)+3.2)/(2+3)=(4)/(5)`
`therefore OP =(1)/(5)(7hat(i)+3hat(j)+4hat(k))`