Question

A fly flies from a point $P(0,4,6)$ to the point $Q(2,1,4)$. The magnitude of displacement covered by it is

• A. $\sqrt{7}$
• B. $\sqrt{17}$
• C. $\sqrt{13}$
• D. $\sqrt{10}$

Answer 1

The correct option is B $\sqrt{17}$

Given, the two points where fly flies, so representing them vectorially we have
$\overrightarrow{P}=4\hat{j}+6\hat{k}$, and $\overrightarrow{Q}=2\hat{i}+\hat{j}+4\hat{k}$
Thus, the displacement covered by it is
$\overrightarrow{PQ}=\overrightarrow{Q}-\overrightarrow{P}$
$\Rightarrow (2-0)\hat{i}+(1-4)\hat{j}+(4-6)\hat{k}=2\hat{i}-3\hat{j}-2\hat{k}$
$\Rightarrow |\overrightarrow{QP}|=\sqrt{2^2+(-3{)}^2+(-2{)}^2}=\sqrt{17}$