Question

Let $ A(1,-1,2) $ and $ B(2,3,-1) $ be two points. If a point $P$ divides $AB$ internally in the ratio $ 2:3, $ then the position vector of $P$ is

• A. $ \frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+\hat{k}) $
• B. $ \frac{1}{\sqrt{3}}(\hat{i}+6\hat{j}+\hat{k}) $
• C. $ \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) $
• D. $ \frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k}) $
• E. $ \frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+9\hat{k}) $

Answer 1

Answer: (D)

The position vector of P
$=\frac{3A+2B}{3+2} $
$=\frac{3(1,-1,2)+2(2,3,-1)}{5} $
$=\frac{(7,3,4)}{5} $
$=\frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k}) $