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

Answer: (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
$OR=\left[\frac{2\times OQ-1\times OP}{2-1}\right]$
$=\left(\frac{2(3\hat{i}+\hat{j}-4\hat{k})-(6\hat{i}+3\hat{j}-2\hat{k})}{1}\right)$
$=\left\{\frac{6\hat{i}+2\hat{j}-8\hat{k}-6\hat{i}-3\hat{j}+2\hat{k}}{1}\right\}$
$=(-\hat{j}-6\hat{k})$