Magnitude of $\left\langle 1, 2, 1\right\rangle$

Find the magnitude (length) of $\mathbf{\vec{u}} = \left\langle 1, 2, 1\right\rangle$.

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 $\left|{1}\right|^{2} + \left|{2}\right|^{2} + \left|{1}\right|^{2} = 6$.

Therefore, the magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{6}$.

The magnitude is $\sqrt{6}\approx 2.449489742783178$A.