Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

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

1)

$$\begin{array}{l}\hat{k}\end{array}$$

2)

$$\begin{array}{l}\hat{i}+\hat{j}\end{array}$$

3)

$$\begin{array}{l}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\end{array}$$

4)

$$\begin{array}{l}\frac{\hat{i}+\hat{j}}{2}\end{array}$$

$$\begin{array}{l}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\end{array}$$

Solution:

$$\begin{array}{l}\hat{R}=\frac{\vec{R}}{\left | R \right |}=\frac{\hat{i}+\hat{j}}{\sqrt{1^{2}+1^{2}}}= \frac{\hat{i}+\hat{j}}{\sqrt{2}}\end{array}$$