mcv4ua_unit_3_lesson_13.pdf - MCV4U-A 13 Introduction to...

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13 MCV4U-A Introduction to Vectors
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Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved. Calculus and Vectors MCV4U-A Lesson 13, page 1 Introduction So far in this course, you have focused on calculus, specifically calculating rates of change and finding derivatives. You now turn your attention to vectors. Did you know that vectors can be applied to computer-game design, economics, genetics, sociology, and cryptography? In this lesson, you will explore real-life situations that can be represented by vectors. You will use vectors to represent quantities and look at various ways to represent vectors. Estimated Hours for Completing This Lesson Introduction to Vectors 1 Equal Vectors 0.5 Representation of Vectors 2 Key Questions 1.5 What You Will Learn After completing this lesson, you will be able to recognize a vector as a quantity with both a magnitude and a direction identify, gather, and interpret information about real-world applications of vectors represent a vector in two-space geometrically as a directed line segment, with directions expressed in different ways represent a vector algebraically using Cartesian and polar coordinates
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Lesson 13, page 2 Calculus and Vectors MCV4U-A Copyright © 2008 The Ontario Educational Communications Authority. All rights reserved. Introduction to Vectors Many of the problems you have solved in mathematics involve quantities, such as the cost of a product, the area of a square, and the volume of a can. These are scalars, quantities that can be represented by a specific number. The value of a scalar is also called its magnitude. Certain quantities need more than just a single value to represent them. These are referred to as vectors. Examples of vectors include forces, velocities, and acceleration. Consider the following examples: a plane flying east at 400 km/h a force of 40 N pulling a bicycle forward Vector quantities require more than a single scalar (number) to represent them. They are defined as follows: A vector is a quantity that has both a magnitude and a direction. Are the following examples of scalars or vectors? the current time the size of a computer hard drive the speed of a train These are all scalars because they are represented by a value that has no direction attached to it. What about a person’s weight? Your first guess may be that it’s a scalar because you think of it in terms of a value, but it is in fact a vector. A person’s weight is the force exerted as a result of gravity and so has both a magnitude and a direction. Try another example. Do you think you can represent wind with a vector? Yes, wind has a direction and a magnitude. For example, the wind is blowing from the east at a speed of 30 km/h.
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