Question

If $\overrightarrow{P}=\hat{i}+3\hat{j}-7\hat{k}$ and $\overrightarrow{Q}=5\hat{i}-2\hat{j}+4\hat{k}$ then the length of the vector $\overrightarrow{PQ}$ is:

• A. $\sqrt{104}$
• B. $\sqrt{162}$
• C. $-29$
• D. $20$

Answer 1

Answer: (B)

$\sqrt{162}$

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

$\therefore$ $|\overrightarrow{PQ}|=\sqrt{16+25+121}=\sqrt{162}$