Question

If $\hat{i}$ and $\hat{j}$ are unit vectors along x – axis and y – axis respectively, the magnitude of vector $\hat{i}$ + $\hat{j}$ will be

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

Answer 1

The correct option is B $\sqrt{2}$

Let $\hat{i}$ and $\hat{j}$ represent the magnitudes of vectors$\hat{i}$ and $\hat{j}$ respectively.
Since $\hat{i}$ and $\hat{j}$ are unit vectors,magnitudes of $\hat{i}=1$ and $\hat{j}=1.$
Therefore, the magnitude of vector $\hat{i}+\hat{j}=\sqrt{{\hat{i}}^2+{\hat{j}}^2}=\sqrt{(1{)}^2+(1{)}^2}=\sqrt{2}.$
Thus the correct choice is (b).