Watch out
Changing the order of components.
Scottish National 5 Mathematics
National 5 Maths Vectors
Use directed line segments and two- or three-dimensional vector components, including magnitude.
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
- Keep components in a consistent order.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Vectors is an assessed part of Scottish National 5 Mathematics in the geometry area. Use directed line segments and two− or three-dimensional vector components, including magnitude.
Keep components in a consistent order.
Add or subtract corresponding components.
Use Pythagoras across the components for magnitude.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
Vector as movement from A to B
Key formulae and rules
- AB = b − a
- |(x, y)| = √(x² + y²)
- |(x, y, z)| = √(x² + y² + z²)
Check
Check the direction and magnitude separately, keeping components in x, y, z order.
Exam tip
Mark the diagram with the values you use, show the formula and finish with the correct length, area or volume units.
Worked examples
Worked example 1
Vectors worked example
Find the magnitude of (2, −3, 6).
- Magnitude = √(2² + (-3)² + 6²)
- = √(4 + 9 + 36)
Answer: 7
Watch out
- Changing the order of components.
- Omitting the square root when finding magnitude.