Finding the Magnitude of a Vector

Find the magnitude of \(\mathbf{v}\) if:

1. \(\mathbf{v} = \langle 3,-4\rangle\)
2. \(\mathbf{v}=\langle 2,3,-1\rangle\)

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

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