A vector describes a quantity which has both magnitude and direction. The most common notations for vectors are to put an arrow over a letter or to make the letter bold. Graphically, a vector is usually represented by an arrow whose length represents the magnitude and the arrowhead its direction. Vectors are drawn between two points, the initial point and the terminal point. For example, if a vector is drawn between $A$ and $B,$ it can be named $\overrightarrow{AB}$ or $\overrightarrow{BA}$ depending on the initial point and terminal point. It is worth noting that $\overrightarrow{BA}$ and $\overrightarrow{AB}$ have the same magnitude, but opposite direction.

The part of the vector that lies on the initial point is called the tail of the vector, and the part that lies on the terminal point is the tip.

A vector can also be written in component form. In two dimensions, this is $⟨x,y⟩.$ Here, the first coordinate is the horizontal component of the vector and the second coordinate is its vertical component.

In the case of a vector in a three-dimensional space, the component form is $⟨x,y,z⟩.$ Here, the coordinates represent the change in the direction of their corresponding axes.