Null vector : A vector obtained by adding two vectors having the same magnitude and mutually opposite directions is called a null vector. A null vector is represented by $\overrightarrow{\mathrm{O}}$.

$\vec{A}-\vec{A}=\overrightarrow{0} \quad \vec{A} / \sqrt{-\vec{A}}$

Null or zero vector has magnitude equal to zero and has no direction. i.e. its direction can not be specified.

By multiplying zero with any vector $\overrightarrow{\mathrm{A}}$ is null vector. Properties of null vector are as below :

$(i)$ $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{O}}=\overrightarrow{\mathrm{A}}$, $(ii)$ $\lambda \overrightarrow{\mathrm{O}}=\overrightarrow{\mathrm{O}}$, $(iii)$ $\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{O}}$

As shown in figure, particle is at $\mathrm{P}$ at $t=0$. Its position vector w.r.t. $\mathrm{O}$ is $\vec{r}$.

Particle is at $\mathrm{P}^{\prime}$ at ' $t$ ' time. Its position vector w.r.t. $\mathrm{O}$ is $\overrightarrow{r^{\prime}}$.

When this particle returns back to $P$ from $P'$, its displacement vector $(\Delta \vec{r}=\overrightarrow{0})$. This is a null vector.