Question

The position vector of a point $R$ which divides the line joining $ P(6,\,3,-2) $ and $ Q(3,1,-4) $ Q(3,1, - 4) in the ratio $ 2:1 $ externally is

• A. $ \hat{i}+3\hat{j}-2\hat{k} $
• B. $ 3\hat{i}-\hat{k} $
• C. $ -\hat{j}-6\hat{k} $
• D. $ 2\hat{i}-\hat{j} $

Answer 1

The Correct Option is C

Let position vector of P and Q are Day
$ OP=6\hat{i}+3\hat{j}-2\hat{k} $ and $ OQ=3\hat{i}+\hat{j}-4\hat{k} $
Now, by section formula
$ OR=\left[ \frac{2\times OQ-1\times OP}{2-1} \right] $
$ =\left( \frac{2(3\hat{i}+\hat{j}-4\hat{k})-(6\hat{i}+3\hat{j}-2\hat{k})}{1} \right) $
$ =\left\{ \frac{6\hat{i}+2\hat{j}-8\hat{k}-6\hat{i}-3\hat{j}+2\hat{k}}{1} \right\} $
$ =(-\hat{j}\,\,-\,6\hat{k}) $