Question

The unit vector along $i+j$ is

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

Answer 1

The correct option is C

$\frac{i+j}{\sqrt{2}}$

Step 1: Given data

Given vector = $i+j$

Step 2: Formula used

Unit vector along the given vector = $\frac{i+j}{|i+j|}$,

where $|i+j|$ is the magnitude of the given vector

Step 3: Calculating the magnitude of the vector

$|i+j|=\sqrt{i^2+j^2+2ij\cos \left({90}^o\right)}$($i$ and $j$ are unit vectors that are perpendicular to each other) $=\sqrt{2}$'

Step 4: Substituting to obtain unit vector along the given vector

Unit vector along the given vector =$\frac{i+j}{\sqrt{2}}$

Hence, option (C) is the correct answer