Magnitude of $\left\langle 1, -3, -4\right\rangle$

Find the magnitude (length) of $\mathbf{\vec{u}} = \left\langle 1, -3, -4\right\rangle$.

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 $\left|{1}\right|^{2} + \left|{-3}\right|^{2} + \left|{-4}\right|^{2} = 26$.

Therefore, the magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{26}$.

The magnitude is $\sqrt{26}\approx 5.099019513592785$A.