A vector carries both size and direction. This chapter of SPM Additional Mathematics has four linked skills, and each one uses the same habit of writing a journey between two points.
What does this chapter cover?
The skills build on each other. Start with component form, because magnitude, parallel vectors and ratios all use it.
| Skill | Question it answers |
|---|---|
| Component and unit-vector form | How do I write a vector and build one from two points? |
| Magnitude and direction | How long is it, and which way does it point? |
| Parallel vectors and collinearity | When do two vectors lie along the same line? |
| Geometric vector ratios | How do I use a ratio on a line in a diagram? |
The page on vector dependence and ratio reasoning goes deeper once these four are secure.
How do the skills connect?
One small example shows the link. A is the point (2, 5) and B is (8, −3). The vector from A to B is AB = OB − OA = (6, −8) = 6i − 8j.
Its magnitude is √(6² + 8²) = 10, so the unit vector along AB is (6i − 8j) ÷ 10 = 0.6i − 0.8j. Any vector parallel to AB is a multiple of 3i − 4j.
Component form built the vector, magnitude measured it, and a multiple described every parallel vector. Ratio questions use the same steps on parts of a line.
Where should I start?
Pick the line that sounds like you.
- AB and BA keep swapping signs: start with component form.
- Lengths and angles go wrong: start with magnitude and direction.
- Collinearity questions feel like guesswork: start with the parallel-vectors lesson.
- Diagrams with ratios such as 2 : 3 look crowded: finish with geometric ratios.
When you have read the lessons, test the whole chapter with the vectors practice set. If you want a teacher to watch your route around a diagram, see online one-to-one Additional Mathematics tuition.