Magnitude of $$$\left\langle -10, 7, -1\right\rangle$$$

The calculator will find the magnitude (length, norm) of the vector $$$\left\langle -10, 7, -1\right\rangle$$$, with steps shown.
$$$\langle$$$ $$$\rangle$$$

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Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle -10, 7, -1\right\rangle$$$.


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 $$$\left|{-10}\right|^{2} + \left|{7}\right|^{2} + \left|{-1}\right|^{2} = 150$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{150} = 5 \sqrt{6}$$$.


The magnitude is $$$5 \sqrt{6}\approx 12.24744871391589$$$A.