Question

Value of C may be, if $\overrightarrow{A}=\frac{2\hat{i}}{5}-\frac{\hat{j}}{5}+\frac{C\hat{k}}{5}$ is a unit vector.

• A. $\sqrt{20}$
• B. $\sqrt{10}$
• C. 20
• D. 5

Answer 1

The correct option is A $\sqrt{20}$

$|\overrightarrow{A}|=1\sqrt{{\left(\frac{2}{5}\right)}^2+{(-\frac{1}{5})}^2+{\left(\frac{C}{5}\right)}^2}=1$
$4+C^2+1=25$
$C=\pm \sqrt{20}$
$C=+\sqrt{20}$
Hence correct option is a.