## Precalculus (6th Edition) Blitzer

The magnitude of the linear combination of the vector is calculated from, $\left\| \mathbf{v} \right\|=\sqrt{{{a}^{2}}+{{b}^{2}}}$ Here, a is the horizontal component of $\mathbf{v}$ and b is the vertical component of $\mathbf{v}$. \begin{align} & \left\| \mathbf{v} \right\|=\sqrt{{{(-1)}^{2}}+{{(-1)}^{2}}} \\ & =\sqrt{1+1} \\ & =\sqrt{2} \end{align} Thus, the magnitude of the vector is $\sqrt{2}$.