The vector sum of three vectors $\overrightarrow{\mathrm{A}}$ $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ it zero. If $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors in the directions of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ ,respectively, then :

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$

$\Rightarrow \overrightarrow{C}=-\left(\overrightarrow{A}+\overrightarrow{B}\right)$

so, $\overrightarrow{C}$ is in the plane of $\overrightarrow{A} and \overrightarrow{B.}$

Given:  $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors in the directions of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ ,respectively.

Hence, $\overrightarrow{C}$ lies in XY-plane.