Write the position vector of a point dividing the line segment joining points A and B with position vectors ` vec a\ a n d\ vec b` externally in the ration 1:4 where ` vec a=2 hat i+3 hat j+4 hat k\ a n d\ vec b=- hat i+ hat j+ hat kdot`

Explanation

The position vector of point `P` which divides the line joining two points `A` and `B` externally in the ratio 1:4 is given by,

`vec{OP}={1(- hat i+ hat j+ hat kdot)-4(2 hat i+3 hat j+4 hat k)}/{1-4}`

`={-9hati-11j-15k}/{-3}`

`=3hati+11/3hatj+5hatk`