Vectors in two dimensions.
Connect geometric arrows with components, then use products, projections and clear vector arguments to solve two-dimensional problems.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Magnitude and direction
Describe both the size and direction of a displacement, including directions outside the first quadrant.
- 02
Vector equality and opposite vectors
Recognise the same vector in different positions and distinguish an opposite vector from an equal-length vector.
- 03
Addition/subtraction and scalar multiplication
Combine directed changes geometrically and algebraically, and interpret the sign of a scalar multiple.
- 04
Component and unit-vector notation
Translate between ordered pairs and basis-vector notation, and build unit vectors without losing direction.
- 05
Position and displacement vectors
Distinguish an object's position from the change between two positions and use vector interpolation.
- 06
Parallelism and collinearity
Use scalar multiples to recognise parallel vectors and prove that three points lie on one line.
- 07
Dot product
Calculate the scalar product and connect its component formula to the angle between two vectors.
- 08
Angle between vectors
Find the smaller angle between directed vectors and distinguish it from the angle between their supporting lines.
- 09
Scalar/vector projections
Resolve a vector along a chosen direction and distinguish the signed scalar component from the projected vector.
- 10
Perpendicularity
Use a zero dot product to find perpendicular directions and unknown components, then apply it to geometric decisions.
- 11
Vector geometry proofs
Build short, justified arguments about midpoints, parallel sides and right angles using position vectors.
Topic review
Revisit the key ideas, then choose a practice paper.