Question

State the following statement is True or False

Position vectors of points P and Q are $\hat{i}+3\hat{j}-7\hat{k}$ and $5\hat{i}-2\hat{j}+4\hat{k}$ respectively, then value of $|PQ|$ is $9\sqrt{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

$\overrightarrow{PQ}=(5\hat{i}-2\hat{j}+4\hat{k})-(\hat{i}+3\hat{j}-7\hat{k})$

$\overrightarrow{PQ}=4\hat{i}-5\hat{j}+11\hat{k}$

$\left|\overrightarrow{PQ}\right|=$ $\sqrt{4^2+{(-5)}^2+{11}^2}$

$\left|\overrightarrow{PQ}\right|=\sqrt{162}=9\sqrt{2}$