Write the position vector of a point dividing the line segment joining points having position vectors ` hat i+ hat j-2 hat k\ a n d\ 2 hat i- hat j+3 hat k` externally in the ratio 2:3.

Explanation

Let `vec{OA}= hat i+ hat j-2 hat k,vec{OB}= 2 hat i- hat j+3 hat k`

The position vector of point `P` which divides the line joining two points `A` and `B` externally in the ratio 2:3 is given by,

`vec{OP}={2(2 hat i- hat j+3 hat k)-3(hat i+ hat j-2 hat k)}/{2-3}`

`={hati-5hatj}/{-1}`

`=-hati+5hatj`