Question

The unit vector along $\hat{i}+\hat{j}$ is:

• A. $\hat{k}$
• B. $\hat{i}+\hat{j}$
• C. $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
• D. $\frac{\hat{i}+\hat{j}}{2}$

Answer 1

The correct option is C $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

Unit vector along$(i+j)is\frac{(i+j)}{|i+j|}$

$|i+j|ismagnitudeof(i+j)$

we know,

i and j are perpendicular to each other

So, $|i+j|=\sqrt{i^2+j^2+2ijcos{90}^o}$

$\sqrt{1+1}=\sqrt{2}$

hence, unit vector along $(i+j)is\frac{(i+j)}{\surd 2}$