P4.7.7 - Scalar product

Use the scalar product a·b = a1b1 + a2b2 + a3b3 and a·b = |a||b| cos θ to calculate angles between lines and identify perpendicular non-zero vectors.

Use scalar product to connect the rule to the data and decision in the question.

This matters because scalar product determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply scalar product to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Scalar product is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.