Magnitude of $$$\left\langle -1, \frac{3}{11}, - \frac{5}{11}, 1, 0\right\rangle$$$
Your Input
Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle -1, \frac{3}{11}, - \frac{5}{11}, 1, 0\right\rangle$$$.
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 $$$\left|{-1}\right|^{2} + \left|{\frac{3}{11}}\right|^{2} + \left|{- \frac{5}{11}}\right|^{2} + \left|{1}\right|^{2} + \left|{0}\right|^{2} = \frac{276}{121}$$$.
Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{\frac{276}{121}} = \frac{2 \sqrt{69}}{11}$$$.
Answer
The magnitude is $$$\frac{2 \sqrt{69}}{11}\approx 1.510295247803286$$$A.
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