|
|
|
|
|
|
|
|
|
|
|
|
Magnitude of $$$\left\langle \frac{211}{69}, - \frac{84}{23}, - \frac{17}{69}, \frac{272}{69}, 1\right\rangle$$$
Your Input
Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle \frac{211}{69}, - \frac{84}{23}, - \frac{17}{69}, \frac{272}{69}, 1\right\rangle$$$.
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 $$$\left|{\frac{211}{69}}\right|^{2} + \left|{- \frac{84}{23}}\right|^{2} + \left|{- \frac{17}{69}}\right|^{2} + \left|{\frac{272}{69}}\right|^{2} + \left|{1}\right|^{2} = \frac{2711}{69}$$$.
Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{\frac{2711}{69}} = \frac{\sqrt{187059}}{69}$$$.
Answer
The magnitude is $$$\frac{\sqrt{187059}}{69}\approx 6.268162017087925$$$A.