Question

The value of $\left(n\right)$ for which vector$\overrightarrow{OA}=\frac{1}{2}\hat{i}+n\hat{j}+\frac{1}{2}\hat{k}$ is a unit vector is

• A. $\pm \frac{1}{\sqrt{3}}$
• B. $\pm \frac{1}{3}$
• C. $\pm \frac{1}{2}$
• D. $\pm \frac{1}{\sqrt{2}}$

Answer 1

The correct option is D $\pm \frac{1}{\sqrt{2}}$

Since, the magnitude of a unit vector$=1$.
If we have a unit vector
$\overrightarrow{AB}=a\hat{i}+b\hat{j}+c\hat{k}$
then its magnitude
$\text{AB}=\sqrt{a^2+b^2+c^2}=1$

Therefore, as per the question data

$\text{OA}=\sqrt{(\frac{1}{2}{)}^2+n^2+(\frac{1}{2}{)}^2}=1$

Solving we get, $n=\pm \frac{1}{\sqrt{2}}$

Hence, option $\left(\text{C}\right)$ is the right choice.