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.