Vector Magnitude Calculator

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

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Your Input

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

Solution

The vector magnitude of a vector is given by the formula $$$\mathbf{\left\lvert\vec{v}\right\rvert} = \sqrt{\sum_{i=1}^{n} \left|{x_{i}}\right|^{2}}$$$, where $$$x_i, i=\overline{1..n}$$$ are the coordinates of the vector.

The sum of squares of the coordinates is $$$\left|{3}\right|^{2} + \left|{4}\right|^{2} + \left|{12}\right|^{2} = 169$$$.

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

Answer

The magnitude is $$$13$$$A.