# Can a vector with a non zero component be zero?

In three dimensional representation, a vector $\overrightarrow{A}$ with three mutually perpendicular components $A_x\hat{i},$ $A_y\hat{j}$ and $A_z\hat{k}$ along X, Y and Z-axis can be represented as,

$\overrightarrow{A}=A_x\hat{i}+A_y\hat{j}+A_z\hat{k}$

and, the magnitude of $\overrightarrow{A}$ is,

$|\overrightarrow{A}|=A=\sqrt{A_x^2+A_y^2+A_z^2}$

Therefore, $A$ can be zero only if all the components $A_x,$ $A_y$ and $A_z$ are zero. Hence, a vector with a non zero component cannot be zero.