Question

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

$-2\hat{i}+3\hat{j}+5\hat{k},7\hat{i}-\hat{k}$

• A. $3\sqrt{14}$
• B. $\sqrt{54}$
• C. $3\sqrt{19}$
• D. $\sqrt{57}$

Answer 1

The correct option is A $3\sqrt{14}$

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 $-2\hat{i}+3\hat{j}+5\hat{k}$, $7\hat{i}-\hat{k}$
Distance $=\sqrt{{(-2-7)}^2+{(3-0)}^2+{(5+1)}^2}$
$=\sqrt{126}$
$=3\sqrt{14}$