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Quick vector-basics map
Core Definitions
Vector Operations
Lines in Vector Form
Q: What does H2 Maths Notes (JC 1-2): 3.1) Basic Properties of Vectors cover? A: Vector notation, magnitude-direction forms, and line representations for H2 Maths Topic 3.1.
Before you revise Keep vector diagrams clean-label initial points, direction arrows, and magnitudes. Many marks are lost to orientation errors or forgetting column-vector format.
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A vector has size and direction.
Write components clearly.
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Position vectors locate points; direction vectors describe movement.
Decide which one the question uses.
100 seconds
Lines need a point and a direction.
Form r=a+λd
with labels.
Concrete example: If A(1,2,−3) and B(4,−1,5), the direction from A to B is OB−OA, not either position vector alone.
Status: SEAB's current H2 Mathematics (9758) syllabus PDF is labelled for 2026. Topic 3.1 focuses on vector notation, basic operations, and vector equations of lines.
Core Definitions
A vector v has magnitude ∥v∥ and direction; in component form v=(v1v2v3).
Want weekly guided practice on Basic Vector Properties? Our H2 Maths tuition programme builds fluency in this topic through structured problem sets and exam-style drills.
Common exam mistakes
Confusing position vectors with direction vectors: A position vector OA points from the origin to a specific point; a direction vector describes orientation along a line with no fixed starting point. Using a position vector as a direction vector (or vice versa) produces a wrong line equation.
Forgetting the parameter range when describing a line segment: The vector equation r=OA+λd describes an infinite line. If the question asks about a finite segment AB, you must state the range 0≤λ≤1; omitting this loses the interpretation mark.
Rounding cosθ before applying arccos: Premature rounding of the dot product result before taking arccos compounds errors. Keep the exact fraction until the final step.
Testing collinearity with only two vectors: To show three points A,B,C are collinear, you need to show AB=kAC
Giving angle as obtuse when the context requires acute: The dot product formula gives the angle between the lines' directions. Always consider whether the geometrically meaningful angle is the acute or obtuse version, and state your reasoning.
Frequently asked questions
Are vectors in Paper 1 or Paper 2? Topic 3 (Vectors) is Pure Mathematics and can appear in Paper 1 (100 marks) or Paper 2 Section A (40 marks). Vector geometry questions are often long-structured questions worth 8–12 marks.
What is the difference between collinearity and coplanarity? Three points are collinear if they all lie on the same line. Four points are coplanar if they all lie in the same plane. To test collinearity, show direction vectors are parallel with a shared point. To test coplanarity, find a plane equation and verify all four points satisfy it.
Do I need to draw a 3D diagram in the exam? Yes. A clear labelled diagram earns method marks and helps you interpret vector relationships correctly. Even a rough 3D sketch showing the line direction, a point, and key vectors is sufficient - precision is less important than clarity.
