Magnitude of 1,3,4\left\langle 1, -3, -4\right\rangle

The calculator will find the magnitude (length, norm) of the vector 1,3,4\left\langle 1, -3, -4\right\rangle, with steps shown.
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Your Input

Find the magnitude (length) of u=1,3,4\mathbf{\vec{u}} = \left\langle 1, -3, -4\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 12+32+42=26\left|{1}\right|^{2} + \left|{-3}\right|^{2} + \left|{-4}\right|^{2} = 26.

Therefore, the magnitude of the vector is u=26\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{26}.

Answer

The magnitude is 265.099019513592785\sqrt{26}\approx 5.099019513592785A.