# How do I find the magnitude of a vector?

The magnitude of a vector in ${\mathbb{R}}^{n}$ (if you're using dot product as inner product) is given by the square-root of the sum of the square of each coordinate of the vector.
Let $v = \left[{v}_{1} , {v}_{2} , {v}_{3} , {v}_{4}\right]$:
The magnitude of $v$ is $\sqrt{{\left({v}_{1}\right)}^{2} + {\left({v}_{2}\right)}^{2} + {\left({v}_{3}\right)}^{2} + {\left({v}_{4}\right)}^{2}}$//
For a more general ${\mathbb{R}}^{n}$ vector $u = \left[{u}_{1} , {u}_{2} , \ldots , {u}_{n}\right]$, its magnitude is given by $\sqrt{{\left({u}_{1}\right)}^{2} + {\left({u}_{2}\right)}^{2} + \ldots + {\left({u}_{n}\right)}^{2}}$//