## Grade 12 Calculus and Vectors

Chapter 7: Introduction to Vectors

By definition, **vector** is a mathematical body that must be described by **magnitude** and **direction**. Magnitude normally represents the size of the vector/body, and direction; well, it indicates the direction or orientation of the vector with respect to a reference. Examples of vectors include displacement, velocity, acceleration and force to name a few.

A more specific example would be, velocity V = 100 km/h [N 45deg E].

A **scalar** can almost be seen as a vector's little brother; as he may be completely described only by his magnitude. Examples of scalars include, distance, speed, area, volume and so on. That’s not to say scalar quantities are useless, but they are not useful in mathematical calculations.

A more specific example of scalar is area A = 5,000 m^{2}

Can you tell the difference between a scalar and a vector? Good, scalar quantities are not described using directions, only described using units that indicates their size (or magnitude).

Review of the trigonometric identities is highly recommended, as all vector questions involves angles (essential for providing direction), and projections of one vector body onto another and etcetera. Also pay close attention to capitalization used in textbooks and classroom notes when writing out a vector. As “**T**” and “**t**” could mean two completely different vectors.

Okay, let’s look at what this chapter will cover:

- Definition and characteristics of vectors

- Properties of vectors

- Two- and Three-Dimensional vector representations in Cartesian coordinates system

- Computations of vectors in two- and three-dimensions

**
7.1 Review of Trigonometric Identities
7.2 Introduction to Vectors
7.3 Adding and Subtracting Vectors
7.4 Multiplication of Vector by Scalar
7.5 Computational Properties of Vectors
7.6 Three-Dimensional Vectors
7.7 2-D Vector Representations & Operations - in Unit Vector and Component Form
7.8 3-D Vector Representations & Operations - in Unit Vector and Component Form
7.9 Linear Combinations and Span of Vectors
**

## Grade 12 Calculus and Vectors

Chapter 1: Introductin to* Calculus *and Vectors

Chapter 2: Derivatives

Chapter 3: Applications of Derivatives

Chapter 4: Curve Sketching

Chapter 5: Derivatives of Trigonometric Functions

Chapter 6: Derivatives of Exponential Functions

Chapter 7: Introduction to * Vectors *

7.1 Review of Trigonometric Identities

7.2 Introduction to Vectors

7.3 Adding and Subtracting Vectors

7.4 Multiplication of Vector by Scalar

7.5 Computational Properties of Vectors

7.6 Three-Dimensional Vectors

7.7 2-D Vector Representations & Operations -

Using Unit Vector and Component Form

7.8 3-D Vector Representations & Operations -

Using Unit Vector and Component Form

7.9 Linear Combinations and Span of Vectors

Chapter 8: Vector Operations and Applications

Chapter 9: Equations of Lines

Chapter 10: Equations of Planes

Chapter 11: Points, Lines and Planes

Videos for each topic contain a playlist, allowing you to choose the instructor and learning style to your liking. You can choose different videos in a topic by placing the mouse over the video and selecting a different video from the playlist. Videos of solutions to multiple example problems are also available to illustrate to students how each tools and techniques should be used.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

## The Courses we offer

- English / French
- Mathematics / Statistics
- Advanced Functions
- Calculus and Vectors
- Algebra and Geometry
- All Science Courses
- Physics / Chemistry / Biology
- Anatomy / Pathophysiology / Kinesiology
- Thermodynamics / Fluids Dynamics
- Pronunciation and Language Help
- Computer Science / Programming
- CAD / Software and Applications Trainings

View all courses and support offered »

## Programs and Services provided

- In-Home 1-on-1 tutoring
- Small Group Neighbourhood tutoring
- Mentoring / Course scheduling
- FREE supplementary Video Tutorials
- Extra practice materials
- Distant learning assistance
- Projects / Workshops / Camps
- Science Competitions
- Accelerated/Enriched programs
- Reinforcement programs

See what sets us apart »