1. Angle between two vectors
Consider two vectors, a and b, and the angle in between them.
The red line can be expressed as:
a - b a b
Use the cosine rule:
This formula is in the information booklet and does not need to be learnt.

2. Scalar (dot) product
The shaded part is known as the dot product of two matrices.
Find the dot product of each of the following. 1. 2. 3.

3. Calculating the angle between two vectors3. 4. 5.
Use the formula to find the angle between each of the following vectors. Give each angle to the nearest degree. 1. 2.
What is special about the vectors in questions 2 and 4?
Vectors are perpendicular.
What about question 3?
Vectors are parallel.

4. Perpendicular and parallel vectors
Which of the following are parallel, perpendicular or neither?
Perpendicular vectors meet at a right angle, where 1. 2. 3. 4. 5.
parallel
neither
If then the two vectors are perpendicular.
perpendicular or
parallel
the vectors are parallel.
perpendicular
Note: Also if one vector is a multiple of another then the two vectors are parallel.