Find the position vector of the mid point of the line segment `A B ,\ ` where `A` is the point (3, 4, -2) and B is the point (1, ,2 4).

Explanation

`vec{OA}= 3hat i+ 4hat j-2 hat k,vec{OB}= hat i+2 hat j+4 hat k`

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

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

`={4hati+6hatj+2hatk}/{2}`

`=2hati+3hatj+hatk`