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SQA National 5 Mathematics

Adding and subtracting vectors

Combining vectors using paths and components.

Formula referenceMixed revision

Formula reference

Check the National 5 rules and formulae linked to this topic.

Which method?

Match exam clues to a suitable method.

Before you start

  • Read the command word and identify what is being asked.
  • Write down the relevant formula, rule or algebraic structure before substituting values.
  • Keep working set out line by line so method marks are clear.
National 5 Mathematics lesson

Explanation

Adding and subtracting vectors is part of Vectors in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.

For adding and subtracting vectors, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.

National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.

Key formulae and rules

  • Calculator and non-calculator methods may both be useful.
  • Vector path rule: AB = b − a when OA = a and OB = b

Watch out

Choosing a method from a remembered keyword instead of reading the whole question.

Check

Check direction and length separately. A correct vector needs both components in the right order.

Exam tip

Method marks come from clear setup and correct mathematical notation, not just a final answer.

Calculator tip

Use brackets for fractions, powers and square roots, then round only at the final line.

Worked examples

Worked example 1

Find a vector from coordinates

A(2, 1) and B(7, 5). Find AB.

  1. Subtract start from destination.
  2. AB = (7 − 2, 5 − 1)

Answer: AB = (5, 4)

Worked example 2

Reverse direction

If AB = (5, 4), find BA.

  1. Reverse the signs of both components.

So: BA = (-5, −4)

Worked example 3

Use position vectors

If OA = a and OB = b, write AB.

  1. Move from A to O: −a.
  2. Move from O to B: b.

Answer: AB = b − a

Watch out

  • Choosing a method from a remembered keyword instead of reading the whole question.
  • Dropping negative signs, powers or brackets during the working.
  • Giving a rounded decimal when an exact answer or algebraic form is needed.