Question

Find the distance between the points whose position vectors are given as follows

$4\hat{i}+3\hat{j}-6\hat{k},-2\hat{i}+\hat{j}-\hat{k}$

• A. $\sqrt{65}$
• B. $\sqrt{69}$
• C. $13$
• D. none of these

Answer 1

Answer: (A)

$\sqrt{65}$

Distance Between two position vectors $a\hat{i}+b\hat{j}+c\hat{k}$ and $x\hat{i}+y\hat{j}+z\hat{k}$ is given by
$\sqrt{{(a-x)}^2+{(b-y)}^2+{(c-z)}^2}$
Given $4\hat{i}+3\hat{j}-6\hat{k}$, $-2\hat{i}+\hat{j}-\hat{k}$
Distance $=\sqrt{{(4+2)}^2+{(3-1)}^2+{(-6+1)}^2}$
$=\sqrt{65}$