Vectors: What is a Vector?

This first tutorial on vectors will explain what vectors are in contrast to scalars in physics

A vector is a quantity that has both magnitude and direction. In other words, when drawn on a graph or diagram, a vector has a certain length (magnitude) and points in a certain direction.

Force is an example of a vector quantity. Every force vector has an amount of force in Newtons, this serves as the magnitude of the vector. Every force vector also includes a direction.

Below are examples of force vectors:

Notice how each force vector has a magnitude specified in Newtons, and how the arrows point in the direction of the force. For example, the normal force (n) is 9.8 N, up. For oblique vectors, such as the above vector for applied force (FA), usually an angle measure is given to specify the direction. The next part in this series will explain more about the direction and magnitude of vectors.

In contrast, a scalar is a quantity that has magnitude, but no specified direction. For an example, length is a scalar quantity. If you had a cube of side lengths of 3 cm, no matter the direction the cube is rotated, the sides will still be 3 cm long. Another example is the mass (m) of the object in the above drawing. The mass of the object does not depend on what direction the object is facing.