Mr R-C's Classes
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  • IGCSE
    • IGCSE Unit Resources >
      • Unit 0 - Simultaneous Equations
      • Unit 0 - Regression
      • Unit 1 - Percentages
      • Unit 2 - Sets
      • Unit 2 - Graphs and GDC
      • Unit 3 - Indices and Surds
      • Unit 4 - Circle Theorems
      • Unit 5 - Formulae
      • Unit 6 - Vectors
      • Unit 7 - Quadratic Equations
      • Unit 8 - Tree Diagrams
      • Unit 9 - Coordinate Geometry
      • Unit 10 - Sequences
      • Unit 11 - Statistical Diagrams
      • Unit 12 - Composite and Inverse Functions
      • Unit 13 - Similarity
      • Unit 14 - Variation
      • Unit 15 - Algebraic Fractions
      • Unit 16 - Advanced Trigonometry
      • Unit 17 - Quadratic Functions
      • Unit 18 - Volumes and Surface Area
      • Unit 19 - Graphs
      • Unit 20 - Logarithms
      • Unit 21 - Transforming Graphs
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  • IB
    • Mathematical Studies >
      • MSSL Unit Resources >
        • Unit 1 - Number Review
        • Unit 2 - Sequences and Series
        • Unit 3 - Statistics 1
        • Unit 4 - Functions 1
        • Unit 5 - Trigonometry and Mensurations
        • Unit 6 - Functions 2
        • Unit 7 - Statistics 2
        • Unit 8 - Differentiation
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        • Unit 11 - Financial Maths
        • Unit 12 - Statistics 3
        • Unit 13 - Logic
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      • HL Unit Resources >
        • Unit 1 - Algebra
        • Unit 2 - Functions & Equations
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        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Statistics and Probability
        • Unit 6 - Differential Calculus
        • Unit 7 - Discrete Probability Distributions
        • Unit 8 - Integral Calculus
        • Unit 9 - Continuous Probability Distributions
        • Unit 10 - Complex Numbers
        • Unit 11A - Statistics Option
        • Unit 11B - Sets and Groups Option
        • Unit 12 - Vectors
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      • AASL Unit Resources >
        • Unit 0 - Proof
        • Unit 1 - Algebra Functions Basics
        • Unit 2 - Functions, Equations and Inequalities
        • Unit 3 - Sequences and Series
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Trigonometric Functions and Equations
        • Unit 6 - Differentiation 1
        • Unit 7 - Statistics
        • Unit 8 - Probability
        • Unit 9 - Mensuration
        • Unit 10 - Differentiation 2
        • Unit 11 - Integration
      • AASL Revision Materials
      • AASL Key Skills Generator

Unit 12 - Vectors

Unit Objectives
Prior Knowledge:
  • Vectors as movements in 2 dimensions
  • Sum, difference, scalar multiplication and magnitude of a vector 
By the end of this unit students should be able to:
  • Understand and use column and component forms of vectors in 2 and 3 dimensions
  • Know that  the vector AB is given by b - a
  • Calculate scalar products
  • Know and use the properties of the scalar product: commutative; distributive over addition; associative with scalar multiplication, scalar product of a vector with itself
  • Find the angle between two vectors (and lines) and identify parallel and perpendicular vectors
  • Understand and use the vector equation of a line
  • Convert to parametric and cartesian equations of lines
  • Solve problems of coincident, parallel, intersecting and skew lines
  • Identify points of intersection
  • Understand and use the definition of the vector product of two vectors
  • Know and use the properties of vector product:  non-commutative, distributive over addition,  associative with scalar multiplication, cross product of a vector with itself.
  • Interpret cross product geometrically
  • Understand and use the vector equation of a plane
  • Use the normal vector to convert between vector and Cartesian equations of planes
  • Find the intersection of: lines with planes, two planes, three planes
  • Find the angle between; a line and a plane, two planes
  • Identify if; unique, non-unique, no – solutions exist to systems of equations. Find solutions when they exist.
Lesson Resources​
1. Vectors Basics
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
2. Vectors in 3D
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
3. Vector Equations of a Straight Line
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
4. Scalar Products
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
5. Vector Product
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
6. Planes
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
7. Angles Between Lines and Planes
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
8. Distance to Lines and Planes
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
9. Intersection of Two Lines or Planes
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
10. Intersection of Three Planes
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
11. Modelling With Vectors
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
12. Vectors Review
Worksheet
For a whole range of mathematical activities for use in and out of the classroom, including random question generators, Bingo generators and worksheet generators, as well as computer based investigations and activities check out my main site: www.interactive-maths.com.

​If you are interested in codes, ciphers and codebreaking, then check out my secondary site, Crypto Corner, dedicated to providing information about all types of ciphers, as well as tools for encrypting, decrypting and breaking messages.
  • Home
  • IGCSE
    • IGCSE Unit Resources >
      • Unit 0 - Simultaneous Equations
      • Unit 0 - Regression
      • Unit 1 - Percentages
      • Unit 2 - Sets
      • Unit 2 - Graphs and GDC
      • Unit 3 - Indices and Surds
      • Unit 4 - Circle Theorems
      • Unit 5 - Formulae
      • Unit 6 - Vectors
      • Unit 7 - Quadratic Equations
      • Unit 8 - Tree Diagrams
      • Unit 9 - Coordinate Geometry
      • Unit 10 - Sequences
      • Unit 11 - Statistical Diagrams
      • Unit 12 - Composite and Inverse Functions
      • Unit 13 - Similarity
      • Unit 14 - Variation
      • Unit 15 - Algebraic Fractions
      • Unit 16 - Advanced Trigonometry
      • Unit 17 - Quadratic Functions
      • Unit 18 - Volumes and Surface Area
      • Unit 19 - Graphs
      • Unit 20 - Logarithms
      • Unit 21 - Transforming Graphs
    • IGCSE Revision Materials
  • IB
    • Mathematical Studies >
      • MSSL Unit Resources >
        • Unit 1 - Number Review
        • Unit 2 - Sequences and Series
        • Unit 3 - Statistics 1
        • Unit 4 - Functions 1
        • Unit 5 - Trigonometry and Mensurations
        • Unit 6 - Functions 2
        • Unit 7 - Statistics 2
        • Unit 8 - Differentiation
        • Unit 9 - Sets and Probability
        • Unit 10 - Functions 3
        • Unit 11 - Financial Maths
        • Unit 12 - Statistics 3
        • Unit 13 - Logic
      • IB Studies Revision Homework
      • MSSL Revision Materials
      • Studies Exam Question Practice
    • Mathematics Higher Level >
      • HL Unit Resources >
        • Unit 1 - Algebra
        • Unit 2 - Functions & Equations
        • Unit 3 - Trigonometry
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Statistics and Probability
        • Unit 6 - Differential Calculus
        • Unit 7 - Discrete Probability Distributions
        • Unit 8 - Integral Calculus
        • Unit 9 - Continuous Probability Distributions
        • Unit 10 - Complex Numbers
        • Unit 11A - Statistics Option
        • Unit 11B - Sets and Groups Option
        • Unit 12 - Vectors
      • HL Revision Materials >
        • HL Weekly Quizzes
    • Mathematics AA SL >
      • AASL Unit Resources >
        • Unit 0 - Proof
        • Unit 1 - Algebra Functions Basics
        • Unit 2 - Functions, Equations and Inequalities
        • Unit 3 - Sequences and Series
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Trigonometric Functions and Equations
        • Unit 6 - Differentiation 1
        • Unit 7 - Statistics
        • Unit 8 - Probability
        • Unit 9 - Mensuration
        • Unit 10 - Differentiation 2
        • Unit 11 - Integration
      • AASL Revision Materials
      • AASL Key Skills Generator