|
Magnitude of $$$\left\langle - \frac{3}{17}, - \frac{4}{17}, \frac{3}{17}\right\rangle$$$
Your Input
Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle - \frac{3}{17}, - \frac{4}{17}, \frac{3}{17}\right\rangle$$$.
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 $$$\left|{- \frac{3}{17}}\right|^{2} + \left|{- \frac{4}{17}}\right|^{2} + \left|{\frac{3}{17}}\right|^{2} = \frac{2}{17}$$$.
Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{\frac{2}{17}} = \frac{\sqrt{34}}{17}$$$.
Answer
The magnitude is $$$\frac{\sqrt{34}}{17}\approx 0.342997170285018$$$A.