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Magnitude of $$$\left\langle -4, -6\right\rangle$$$

The calculator will find the magnitude (length, norm) of the vector $$$\left\langle -4, -6\right\rangle$$$, with steps shown.
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Your Input

Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle -4, -6\right\rangle$$$.

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 $$$\left|{-4}\right|^{2} + \left|{-6}\right|^{2} = 52$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{52} = 2 \sqrt{13}$$$.

Answer

The magnitude is $$$2 \sqrt{13}\approx 7.211102550927979$$$A.