Magnitude of $$$\left\langle -4, 5, 7\right\rangle$$$
Your Input
Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle -4, 5, 7\right\rangle$$$.
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 $$$\left|{-4}\right|^{2} + \left|{5}\right|^{2} + \left|{7}\right|^{2} = 90$$$.
Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{90} = 3 \sqrt{10}$$$.
Answer
The magnitude is $$$3 \sqrt{10}\approx 9.486832980505138$$$A.