## Precalculus (6th Edition) Blitzer

The one similarity between the zero vector and the number $0$ is that they have the same magnitude and that is equal to zero.
Since, the $\vec{0}$ is written as, $\vec{0}=\vec{0}\text{i}+\vec{0}\text{j}$ The magnitude of the vector $\vec{v}=a\text{i + }b\text{j}$ is, $\left| {\vec{v}} \right|=\sqrt{{{a}^{2}}+{{b}^{2}}}$ So, the magnitude of the vector $\vec{0}$ is, \begin{align} & \left| {\vec{0}} \right|=\sqrt{{{0}^{2}}+{{0}^{2}}} \\ & =0 \end{align} The magnitude of a scalar quantity is equal to the mode of itself. Since the number $0$ is a scalar quantity, so, the magnitude of $0$ is $0$. So, the zero vector and number $0$ have the same magnitude and that magnitude is equal to zero.