Find the magnitude of $\mathbf{v}$ if:

Solution (a) $\Vert \mathbf{v}\Vert = \sqrt{v_{1}^{2}+v_{2}^{2}} = \sqrt{3^{2}+(-4)^{2}} = \sqrt{9+16} = 5$

(b) $\Vert \mathbf{v}\Vert = \sqrt{v_{1}^{2} + v_{2}^{2} + v_{3}^{2}} = \sqrt{2^{2} + 3^{2} + (-1)^{2}} = \sqrt{4 + 9 + 1} = \sqrt{14}$