Introduction to Vectors
Build vector notation, operations, dot products, projections and practical vector applications.
Active lessons
8
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 7 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
8 of 8 active
Lesson 1
Vectors, Scalars and Notation
Define vectors and scalars, use column and i, j notation, and calculate magnitudes and unit vectors.
Lesson 2
Vector Addition and Subtraction
Add, subtract and scale vectors using component methods and geometric interpretations.
Lesson 3
The Dot Product
Use the dot product to find scalar products, angles between vectors, and perpendicularity.
Lesson 4
Vector Projections and Applications
Calculate scalar and vector projections and apply them to force, velocity and displacement contexts.
Lesson 5
Proof of the Projection Formula and Perpendicular Component
Derive the projection formula from the perpendicularity condition, find the perpendicular component of a vector, verify the decomposition using the dot product, and write the full parallel + perpendicular decomposition.
Lesson 6
Vector Functions of Time: Position, Velocity and Acceleration
Represent the position of a moving point as r(t) = (x(t), y(t)), differentiate to find the velocity and acceleration vectors, compute speed |v(t)|, and find position from velocity by integration.
Lesson 7
Projectile Motion in Vector and Parametric Form
Model projectile motion as r(t) = (Vcosθ·t, Vsinθ·t − ½gt²), find velocity by differentiation, determine time of flight, maximum height, range, and impact velocity, and solve problems where launch speed or angle is unknown.
Lesson 8
Prior Knowledge Revision: Scalars, Vectors and Distance
Activate prior knowledge for vectors: distinguish scalar and vector quantities, find vector magnitude using Pythagoras, apply the distance formula, and resolve a vector into components using bearings.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.