# Vector Magnitude Calculator

An online calculator for finding the magnitude (length, norm) of a vector, with steps shown.

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Find the magnitude (length) of $\mathbf{\vec{u}} = \left\langle 3, 4, 12\right\rangle$.

## 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 $\left|{3}\right|^{2} + \left|{4}\right|^{2} + \left|{12}\right|^{2} = 169$.

Therefore, the magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{169} = 13$.

The magnitude is $13$A.