Question

Find the unit vector in the direction of the vector $x\hat{i}+y\hat{j}$.

Answer 1

Let $\overrightarrow{r}=x\hat{i}+y\hat{j}$.

Now the unit vector in the direction of $\overrightarrow{r}$ is $\frac{\overrightarrow{r}}{|\overrightarrow{r}|}=\frac{x\hat{i}+y\hat{j}}{\sqrt{x^2+y^2}}$..