Vector
A vector is a quantity that has both magnitude (size or length) and direction. In mathematics and physics, it is typically represented by a directed line segment or an arrow.
Example
A vector $\mathbf{v}$ moving $3$ units right and $4$ units up can be written as a column vector $\begin{pmatrix} 3 \\ 4 \end{pmatrix}$. Its magnitude is $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$.