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 m²

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