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

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

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

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

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 $$$\left|{-6}\right|^{2} + \left|{6}\right|^{2} = 72$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{72} = 6 \sqrt{2}$$$.

Answer

The magnitude is $$$6 \sqrt{2}\approx 8.48528137423857$$$A.