Magnitude of $$$\left\langle 2, 1, -1\right\rangle$$$
Your Input
Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle 2, 1, -1\right\rangle$$$.
Solution
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 $$$\left|{2}\right|^{2} + \left|{1}\right|^{2} + \left|{-1}\right|^{2} = 6$$$.
Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{6}$$$.
Answer
The magnitude is $$$\sqrt{6}\approx 2.449489742783178$$$A.