If `barp=hati-2hatj+hatkand barq =hati+4hatj-2hatk` are position vector (P,V.) of points P and Q find the position internally in the ratio 2:1.

Explanation

Let R `(vecr)` is the point which divides th line segment joining the points P and Q internally in the ratio `2:1.`
`vecr=(2(hati+4hatj-2hatk)+1(hati-2hatj+hatk))/(2+1)`
`vecr=(3hati+6hatj-3hatk)/(3)`
`thereforevecr=hati+2hatj-hatk`
and the coordinates of the point R are `(1,2-1).`