Assertion : If $\hat{i}$ and $\hat{j}$ are unit vectors along $x$-axis and $y$-axis respectively, th

Question

Assertion : 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 $\sqrt{2}$.\ Reason : Unit vectors are used to indicate direction only.

Professor PC Thomas Classes · Answer

(b) : Since $\hat{i}$ and $\hat{j}$ are unit vectors, their magnitude are $|\hat{i}|=1$ and $|\hat{j}|=1$. Magnitude of resultant vector is equal to $\sqrt{|\hat{i}|^2+|\hat{j}|^2}=\sqrt{(1)^2+(1)^2}=\sqrt{2}$