Magnitude of $$$\left\langle 1, 3, 2 t\right\rangle$$$

The calculator will find the magnitude (length, norm) of the vector $$$\left\langle 1, 3, 2 t\right\rangle$$$, with steps shown.
$$$\langle$$$ $$$\rangle$$$

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 $$$\mathbf{\vec{u}} = \left\langle 1, 3, 2 t\right\rangle$$$.


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 $$$\left|{1}\right|^{2} + \left|{3}\right|^{2} + \left|{2 t}\right|^{2} = 4 t^{2} + 10$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{4 t^{2} + 10}$$$.


The magnitude is $$$\sqrt{4 t^{2} + 10}\approx 3.162277660168379 \left(0.4 t^{2} + 1\right)^{0.5}$$$A.