Magnitude of 4,5,7\left\langle -4, 5, 7\right\rangle

The calculator will find the magnitude (length, norm) of the vector 4,5,7\left\langle -4, 5, 7\right\rangle, with steps shown.
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Your Input

Find the magnitude (length) of u=4,5,7\mathbf{\vec{u}} = \left\langle -4, 5, 7\right\rangle.

Solution

The vector magnitude of a vector is given by the formula u=i=1nui2\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 42+52+72=90\left|{-4}\right|^{2} + \left|{5}\right|^{2} + \left|{7}\right|^{2} = 90.

Therefore, the magnitude of the vector is u=90=310\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{90} = 3 \sqrt{10}.

Answer

The magnitude is 3109.4868329805051383 \sqrt{10}\approx 9.486832980505138A.