Scalars and Vectors

What is a Vector?

A vector is a physical quantity that has both magnitude (size) and direction.

Examples of Vectors: Displacement, velocity, force, acceleration and momentum.

What is a Scalar?

A scalar is a physical quantity that has magnitude only (it doesn’t act in a certain direction).

Examples of Scalars: Distance, speed, energy, power, pressure, temperature and mass.


Vector Diagrams

A vector can be represented by a vector diagram as well as numerically:

The length of the line represents the magnitude of the vector.

The direction of the line represents the direction of the vector.

We can see that vector a has a greater magnitude than vector b but acts in a different direction.

A negative vector means a vector of equal magnitude but opposite direction.


Adding Vectors

We can add vectors together to find the affect that two or more would have if acting at the same time. This is called the resultant vector. We can find the resultant vector in four ways: Scale drawing, Pythagoras, the Sine and Cosine rules and Resolving vectors (next lesson).


Scale Drawing

To find the resultant vector of a + b we draw vector a then draw vector b from the end of a. The resultant is the line that connects the start and finish points.

The resultants of a + b, b a, a b, a b and would look like this:


If the vectors were drawn to scale we can find the resultant by measuring the length of the line and the angle.



If two vectors are perpendicular to each other the resultant can be found using Pythagoras:

Vector z is the resultant of vectors x and y.

Since x and y are perpendicular     à

We can also use this in reverse to find x or y: