What Is a Vector?

A vector has both length (often called size) and direction, and can be interpreted as a displacement in the plane. Normal numbers that you otherwise work with, those without direction, are called scalars in this context. Two vectors are equal if they have the same length and the same direction. Vectors can be moved around in the plane without changing as long as you don’t change their length and direction.

A vector can be written as a letter with an arrow above it, $\overrightarrow{v}$, or as a coordinate. Vector coordinates can be written with parentheses just like normal coordinates ($\left(x,y\right)$), with brackets ($[x,y]$) or with angle brackets ($⟨x,y⟩$). On this site we will be using the normal parentheses. Vectors in the plane have two coordinates, because the plane has two axes.

Note! The plane is another name for the coordinate system with the first axis and the second axis.