What is unit vector ? Explain.

The vector whose magnitude is $1$ unit is called unit vector.

It represents the direction.

It doesn't have any unit or dimensions.

In Cartesian coordinate system, unit vectors of $x, y, z$ axes are $\hat{i}, \hat{j}, \hat{k}$ respectively.

As magnitude of unit vector is $1$ ,

$|\hat{i}|=|\hat{j}|=|\hat{k}|=1$

These vectors are perpendicular to each other.

Unit vector can be obtained by dividing vector with its magnitude.

Example : If unit vector of $\vec{A}$ is $\hat{n}$, then

$\hat{n}=\frac{\overrightarrow{\mathrm{A}}}{|\overrightarrow{\mathrm{A}}|}=\frac{\overrightarrow{\mathrm{A}}}{\mathrm{A}}=\frac{\text { vector }}{\text { magnitude of vector }}$

According to this equation $\vec{A}=|\vec{A}| \cdot \hat{n}$

Vector $=$ (Magnitude of vector) (Its unit vector)

E.g. : " $5 \mathrm{~N}$ force is acting in $\mathrm{X}$-axis." This can be represented as : $\overrightarrow{\mathrm{F}}=5 \hat{i} \mathrm{~N}$