Magnitude of $\left\langle 5, -2, 3\right\rangle$

Find the magnitude (length) of $\mathbf{\vec{u}} = \left\langle 5, -2, 3\right\rangle$.

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 $\left|{5}\right|^{2} + \left|{-2}\right|^{2} + \left|{3}\right|^{2} = 38$.

Therefore, the magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{38}$.

The magnitude is $\sqrt{38}\approx 6.164414002968976$A.