Vectors

Castro José, Dec 20, 2020

Livret introductif aux vecteurs

Table of Contents

  1. Introduction
    1. Vectors: Introduction (1)
    2. Vectors: Magnitude & Direction (I)
  2. Opérations sur les vecteurs
    1. How to add vectors geometrically
    2. Quiz Practise: Vector Addition
    3. How to subtract vectors geometrically:
    4. Quiz: Vector subtraction
    5. How to multiply a vector by a scalar:
  3. Relation de Chasles
    1. Charles Relation Animation
    2. Relation de Chasles. Vecteurs.
  4. Application
    1. Inclined Plane: An example of how vectors can be useful:

1.

Introduction

  • 1. Vectors: Introduction (1)
  • 2. Vectors: Magnitude & Direction (I)

1.1.

Vectors: Introduction (1)

Recall a [b]VECTOR[/b] is a quantity with [b]both MAGNITUDE and DIRECTION. [/b][br][br]The applet below illustrates how we GEOMETRICALLY represent a vector.[br][br]Interact with this applet for a few minutes. [br]Then, complete the investigation questions you received at the beginning of class.
– Tim Brzezinski

1.2.

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2.

Opérations sur les vecteurs

  • 1. How to add vectors geometrically
  • 2. Quiz Practise: Vector Addition
  • 3. How to subtract vectors geometrically:
  • 4. Quiz: Vector subtraction
  • 5. How to multiply a vector by a scalar:

2.1.

How to add vectors geometrically

[b]Students:[/b][br][br]This applet will help you discover how we geometrically add any 2 vectors. This applet also accompanies the [i][color=#0000ff]Adding Vectors: Introduction[/color][/i] packet you received at the beginning of class. [br][br][b]To Use:[/b][br][br]1) Determine the components of vectors [b]u[/b] and [b]v[/b] by using the [b][color=#9900ff]purple[/color][/b] and [b][color=#38761d]green[/color][/b] sliders. [br]2) Slide the black slider (bottom right) to geometrically form vectors [b]u[/b] and [b]v. [br][/b]3) Move the [b][color=#bf9000]YELLOW POINT[/color][/b] (initial point of [b]v[/b]) ON TOP OF the [b][color=#ff7700]ORANGE POINT[/color][/b] (terminal point of [b]u[/b]). [br][br]4) Slide the additional slider that appears once you complete step (3). [br] The vector that appears will be the the [b]RESULTANT VECTOR[/b]. [br] In this case, the [b]RESULTANT VECTOR[/b] is the sum of vectors [b]u[/b] and [b]v[/b]. [br][br]
Quick (Silent) Demo
– Castro José, Tim Brzezinski

2.2.

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2.3.

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2.4.

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2.5.

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3.

Relation de Chasles

  • 1. Charles Relation Animation
  • 2. Relation de Chasles. Vecteurs.

3.1.

Charles Relation Animation

– Castro José, Daniel Mentrard

3.2.

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4.

Application

  • 1. Inclined Plane: An example of how vectors can be useful:

4.1.

Inclined Plane: An example of how vectors can be useful:

Vectors can be used to represent many things.[br]However, vectors in physics are mainly used to represent forces and by doing this it enables us to use mathematics to describe physics phenomena. [br][br]Here's an example. A body that glides through an incline plane. By clicking the "Show Free Body Diagrams" you can the the vectorial representation of the problem.
– Dinesh, Castro José

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