Magnitude of $$$\left\langle -3, 3\right\rangle$$$

Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle -3, 3\right\rangle$$$.

The vector magnitude of a vector is given by the formula $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{\sum_{i=1}^{n} \left|{u_{i}}\right|^{2}}$$$.

The sum of squares of the absolute values of the coordinates is $$$\left|{-3}\right|^{2} + \left|{3}\right|^{2} = 18$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{18} = 3 \sqrt{2}$$$.

The magnitude is $$$3 \sqrt{2}\approx 4.242640687119285$$$A.