Question

Find the position vector of a point R which divides the line segment joining points:

\[P \left( \hat{i} + 2 \hat{j} + \hat{k}\right) \text { and } Q \left( - \hat{i} + \hat{j} + \hat{k} \right)\] externally

Answer 1

Given:  R divides the line segment joining the points

\[P\left( \hat{i} + 2 \hat{j} + \hat{k} \right) , Q\left( - \hat{i} + \hat{j} + \hat{k}\right)\] in the ratio 2 : 1 externally.
   Therefore. position vector of R = \[\frac{2\left( - \hat{i} +\hat{ j} + \hat{k} \right) - 1\left( \hat{i} + 2 \hat{j} + \hat{k} \right)}{2 - 1}\]

= \[- 3 \hat{i} + \hat{k}\]