# Vector

Formally something that has both direction and length but in practice, computationally speaking, usually a set of Cartesian coordinates. For example
$\mathbf{v} = \begin{pmatrix} v_0\\ v_1\\ v_2 \end{pmatrix}$
Given a number $$x$$ and vectors $$\mathbf{v}$$ and $$\mathbf{w}$$ and denoting the $$i^{th}$$ element of a vector $$\mathbf{v}$$ with $$v_i$$ the rules of vector arithmetic are given by
\begin{align*} (\mathbf{v} \times x)_i &= v_i \times x\\ (x \times \mathbf{v})_i &= v_i \times x\\ \\ (\mathbf{v} \div x)_i &= v_i \div x\\ \\ (\mathbf{v} + \mathbf{w})_i &= v_i + w_i\\ (\mathbf{v} - \mathbf{w})_i &= v_i - w_i\\ \\ \mathbf{v} \times \mathbf{w} &= \sum_i v_i \times w_i \end{align*}
where $$\sum$$ is the summation sign.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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