Question

If $\hat{i}$ and $\hat{j}$ are unit vectors along X-axis and Y-axis respectively, then what is the magnitude and direction of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$ ?

Answer 1

Magnitude of $\hat{i}+\hat{j}$ $=\sqrt{1^2+1^2}=\sqrt{2}$

Direction, $\tan \theta =\frac{1}{1}=1$

$⟹\theta ={45}^o$

So, $\hat{i}+\hat{j}$ makes ${45}^o$ angle with the X-axis.

Magnitude of $\hat{i}-\hat{j}$ $=\sqrt{1^2+1^2}=\sqrt{2}$

Direction, $\tan \theta =\frac{-1}{1}=-1$

$⟹\theta ={135}^o$

So, $\hat{i}-\hat{j}$ makes ${135}^o$ angle with the X-axis.