Vectors are geometric representations of magnitude and direction and can be expressed as arrows in two or three dimensions.
Scalars are physical quantities represented by a single number, and vectors are represented by both a number and a direction.
Vectors may be added or subtracted graphically by laying them end to end on a set of axes.
It is often simpler to add or subtract vectors by using their components.
Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.
Multiplying a vector by a scalar is the same as multiplying its magnitude by a number.
Position, displacement, velocity, and acceleration can all be shown vectors since they are defined in terms of a magnitude and a direction.