Vectors in Three Dimensions
3D vector operations, dot product and angles, equations of lines, and applied exam-style vector problems.
Active lessons
6
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
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
6 of 6 active
Lesson 1
Vectors and Points in 3D
Practise vectors and points in 3d with concise examples and mastery checks.
Lesson 2
Dot Product and Angle
Practise dot product and angle with concise examples and mastery checks.
Lesson 3
Equations of Lines in 3D
Practise equations of lines in 3d with concise examples and mastery checks.
Lesson 4
Vector Applications and Exam Practice
Practise vector applications and exam practice with concise examples and mastery checks.
Lesson 5
Vector Equations of Curves, Circles and Spheres
Represent parametric curves as vector equations, recognise the vector forms of circles and spheres, and convert between vector and Cartesian forms.
Lesson 6
Geometric Proofs Using Vectors
Use dot product identities — including a·a = |a|², distributivity, and the Cauchy–Schwarz inequality — to prove geometric results about triangles and quadrilaterals.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.