Question

Find the position vector of a point R which divides the line segment joining points \[P \left( \hat{i} + 2 \hat{j} + \hat{k} \right) \text{ and Q }\left( - \hat{i} + \hat{j} + \hat{k} \right)\] internally 2:1.

Answer 1

Here `veca = hati + 2hatj + hatk` and `vecb = hat-i + hatj + hatk`

The position vector of R, dividing the join of P and Q internally in the ratio 2:1 is

`vecR = (mvecb + nveca)/(m + n)`

`= (2 (vecb) + 1 (veca))/(2 + 1)`

`= (2 (- hati + hatj + hatk) + 1(hati + 2hatj - hatk))/ (2 + 1)`

`= (-1)/3 hati + 4/3 hatj + 1/3hatk.`