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Paper 2
Advanced Vectors
Both
Use arrow notation for direction and magnitude.
Key Facts
- Parallel vectors are scalar multiples.
- Collinear points lie on the same straight line.
- Magnitude = √(x² + y²)
- Midpoint of AB = (a + b)/2
Key Equations
|v| = √(x² + y²)
Midpoint = (a + b)/2
Topics Covered
Vector Proof
What you need to know
- •Use vector equations to show parallel or intersection points.
- •Position vectors describe locations relative to origin.
- •Displacement vectors describe movement between points.
Exam Tips
- Define position vectors before solving.
- Label points clearly on diagrams.
Vector Geometry
What you need to know
- •Show collinearity by proving vectors are scalar multiples.
- •Find midpoints using (a + b)/2.
- •Prove shapes using properties like parallel sides.
Exam Tips
- Use ratio notation for dividing lines.
Magnitude and Direction
What you need to know
- •Magnitude of (x, y) is √(x² + y²).
- •Unit vectors have magnitude 1.
- •Direction can be found using trigonometry.
Exam Tips
- Always simplify surds in magnitude answers.
Key Terms
Position vector
Vector from the origin to a point.
Displacement vector
Vector representing movement from one point to another.
Collinear
Points that lie on the same straight line.
Unit vector
Vector with magnitude 1.
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Common Exam Questions
Show that vectors (6,9) and (2,3) are parallel.
2 markseasyPaper 2
Model Answer
(6,9) = 3(2,3), so they are parallel.
What examiners want to see
- ✓State scalar multiple clearly.
Points A, B, C have position vectors (1,2), (4,6), (7,10). Show they are collinear.
3 marksmediumPaper 2
Model Answer
AB = (3,4). BC = (3,4). AB = BC so collinear.
What examiners want to see
- ✓Find displacement vectors.
- ✓Show they are equal or multiples.
Find the magnitude of vector (3, -4).
2 markseasyPaper 2
Model Answer
√(9 + 16) = √25 = 5
What examiners want to see
- ✓Use Pythagoras formula.
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