Question

If $\overrightarrow{a}=3\hat{i}-2\hat{j}+\hat{k}$ and $\overrightarrow{b}=2\hat{i}-4\hat{j}-3\hat{k}$, find $|\overrightarrow{a}-2\overrightarrow{b}|$.

• A. $86$
• B. $\sqrt{86}$
• C. $\sqrt{72}$
• D. $72$

Answer 1

The correct option is B $\sqrt{86}$

$\overrightarrow{a}-2\overrightarrow{b}=(3\hat{i}-2\hat{j}+\hat{k})-2(2\hat{i}-4\hat{j}-3\hat{k})=-\hat{i}+6\hat{j}+7\hat{k}$

Therefore,

$|\overrightarrow{a}-2\overrightarrow{b}|=|-\hat{i}+6\hat{j}+7\hat{k}|=\sqrt{(-1{)}^2+6^2+7^2}=\sqrt{86}$