• A scalar is anything that only has a size. Examples might be: mass, temperature.
• A vector is anything that has a size AND a direction. Examples might be: force, acceleration.
• The posh word for ‘size’ is magnitude.

• A scalar has magnitude only.
• A vector has magnitude AND direction.

• We can use arrow diagrams to draw vectors. Sometimes they are called ‘directed line segments’.
• The diagrams tell us the MAGNITUDE of the vector (its length) and the DIRECTION of the vector (its direction).

In the diagram if 1 square is equal to 10N (10 Newtons) then arrow a shows a vector of 40N to the right, and arrow b shows a vector of 50N to the left.

ALWAYS USE A PENCIL AND RULER WHEN DRAWING ARROW DIAGRAMS

Always make sure your diagram is the correct length and include a scale to show how much force each centimetre in your diagram represents (for example 1cm = 10N)

• When we add vectors, we have to take the direction into account.
• Vectors in the same direction ADD.
• Vectors in opposite directions CANCEL.

Here you can see 3 examples of combining vectors together. The top one adds vectors that show forces acting in the same direction (added together). The middle diagrams show two forces acting against each other (in opposite directions) so they are subtracted. The bottom diagrams show two forces acting in the same direction and again being added together.