## Course curriculum

• 1

### A Note before we start

• A Note before we start

• 2

### 5.1 Three Dimensional Vectors

• Vectors in Three Dimensions

• Three-dimensional Coordinate System

• Example 1

• Example 1 Video

• Basic Calculations

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Scalar (Dot) Product of Vectors

• Example 4

• Example 4 Video

• Angle Between Two Vectors

• Example 5

• Example 5 Video

• Parallel & Perpendicular Vectors

• Exercise 5.1

• Exercise 5.1 Recorded Solutions

• 3

### 5.2 Geometric Proofs

• Geometric Proofs in the Plane

• Example 1

• Example 1 Video

• Geometric Proofs in Three Dimensions

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Exercise 5.2

• Exercise 5.2 Recorded Solutions

• 4

### 5.3 Vector Equation of a Line

• Vector Equation of a Line

• Sketching a Vector Equation

• Example 1

• Example 1 Video

• Sketching an Interval

• Example 2

• Example 2 Video

• Finding a Vector Equation of a Line Through Two Points

• Example 3

• Example 3 Video

• Parallel and Perpendicular Lines

• Example 4

• Example 4 Video

• Example 5

• Example 5 Video

• Exercise 5.3

• Exercise 5.3 Recorded Solutions

• 5

### 5.4 Properties of Lines

• Does a Point lie on a Line?

• Example 1

• Example 1 Video

• Point of Intersection

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Converting between Cartesian and Vector Equations

• Example 4

• Example 4 Video

• Exercise 5.4

• Exercise 5.4 Recorded Solutions

• 6

### 5.5 Spheres and Basic Two Dimensional Curves

• Spheres

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Curves in Two Dimensions

• Transformations

• Example 3

• Example 3 Video

• Restrictions

• Example 4

• Example 4 Video

• Spirals

• Example 5

• Example 5 Video

• Exercise 5.5

• Exercise 5.5 Recorded Solutions

• 7

### 5.6 Harder Two Dimensional Curves and Three Dimensional Curves

• Harder Two Dimensional Curves

• Example 1

• Example 1 Video

• Curves in Three Dimensions

• Example 2

• Example 2 Video

• Helices

• Example 3

• Example 3 Video

• Helices & Unusual Curves

• Example 4

• Example 4 Video

• Example 5

• Example 5 Video

• Exercise 5.6

• Exercise 5.6 Recorded Solutions

## Instructor Steven Howard

Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the new syllabus, which you can access from any of his courses. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn't for him, so he went back to uni to retrain as a maths teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!