Chapter 5 - Vectors
This is one of 7 courses which cover the Extension 2 Mathematics Syllabus in NSW.
This set of 7 courses covers the Extension 2 Mathematics Syllabus in NSW.
This is a free course.
Course curriculum
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1
Changes to this content in the 2024 syllabus
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Vectors intro
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2
5.1 Three Dimensional Vectors
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2024 syllabus changes for this lesson
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Vectors in Three Dimensions
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Three-dimensional Coordinate System
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Example 1
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Example 1 Video
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Basic Calculations
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Scalar (Dot) Product of Vectors
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Example 4
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Example 4 Video
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Angle Between Two Vectors
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Example 5
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Example 5 Video
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Parallel & Perpendicular Vectors
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Exercise 5.1
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Exercise 5.1 Recorded Solutions
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3
5.2 Geometric Proofs
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2024 syllabus changes for this lesson
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Geometric Proofs in the Plane
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Example 1
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Example 1 Video
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Geometric Proofs in Three Dimensions
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Example 4
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Example 4 Video
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Exercise 5.2
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Exercise 5.2 Recorded Solutions
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4
5.3 Vector Equation of a Line
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2024 syllabus changes for this lesson
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Vector Equation of a Line
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Sketching a Vector Equation
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Example 1
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Example 1 Video
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Sketching an Interval
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Example 2
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Example 2 Video
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Finding a Vector Equation of a Line Through Two Points
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Example 3
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Example 3 Video
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Parallel and Perpendicular Lines
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Exercise 5.3
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Exercise 5.3 Recorded Solutions
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5
5.4 Properties of Lines
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2024 syllabus changes for this lesson
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Does a Point lie on a Line?
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Example 1
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Example 1 Video
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Point of Intersection
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Converting between Cartesian and Vector Equations
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Example 4
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Example 4 Video
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Exercise 5.4
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Exercise 5.4 Recorded Solutions
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6
5.5 Spheres and Basic Two Dimensional Curves
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2024 syllabus changes for this lesson
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Spheres
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Curves in Two Dimensions
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Transformations
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Example 3
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Example 3 Video
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Restrictions
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Example 4
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Example 4 Video
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Spirals
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Example 5
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Example 5 Video
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Exercise 5.5
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Exercise 5.5 Recorded Solutions
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7
5.6 Harder Two Dimensional Curves and Three Dimensional Curves
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2024 syllabus changes for this lesson
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Harder Two Dimensional Curves
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Example 1
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Example 1 Video
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Curves in Three Dimensions
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Example 2
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Example 2 Video
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Helices
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Example 3
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Example 3 Video
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Helices & Unusual Curves
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Exercise 5.6
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Exercise 5.6 Recorded Solutions
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Instructor
Steve Howard
Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.