This task is designed to provide a route in to more demanding problems on the properties of scalar product. This isn’t a particularly hard topic, but often pupils don’t perform well on it.

The first question is focused entirely on drawing attention to the relevance of the directions of the vectors.

The second question looks at the obtuse angle case. It is necessary for pupils to be able to find cos of an obtuse angle without a calculator for these related exact values.

The 3rd and 4th question build up the basic properties of distribution, a.a and perpendicular vectors.

Credit: @chrismcgrane84