How to (4): Vectors, CAS and 3D views

GeoGebra Institute of MEI, Dec 7, 2015

Table of Contents

  1. Introduction
    1. Introduction to Vectors, Graphics 2 and 3D views
  2. Examples
    1. Expanding cubics
    2. Resolving forces down a plane
  3. Skills
    1. CAS view
    2. Vectors
    3. 3D view
  4. Constructions
    1. Velocity vectors
    2. Vector equation of a line in 3D
  5. Tasks
    1. Suggested tasks

1.

Introduction

  • 1. Introduction to Vectors, Graphics 2 and 3D views

1.1.

Introduction to Vectors, Graphics 2 and 3D views

In this lesson you will be introduced to how GeoGebra handles vectors, and learn about the Graphics 2 and 3D views.[br][br]Some examples of GeoGebra files are displayed in section 2 to give you a sense of what can be achieved.  You should then work through the skills and constructions section before trying the tasks.
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2.

Examples

  • 1. Expanding cubics
  • 2. Resolving forces down a plane

2.1.

Expanding cubics

Expanding cubics
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2.2.

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3.

Skills

  • 1. CAS view
  • 2. Vectors
  • 3. 3D view

3.1.

CAS view

The CAS view can be used to perform algebraic techniques such as solving, factorising, expanding, differentiating and integrating.[br][br]Try entering some expressions and using the buttons.
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3.2.

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3.3.

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4.

Constructions

  • 1. Velocity vectors
  • 2. Vector equation of a line in 3D

4.1.

Velocity vectors

Construction steps
[list=1][*]Add a slider and name it [b]t[/b].[br][/*][*]Using the input bar enter: [b]P=(2-4t,-8+8t)[/b]. [br][/*][*]Using the input bar enter: [b]v=(-4,8)[/b][br][/*][*]Select Vector from point (3rd menu) then select [b]P[/b] and [b]v[/b].[br][/*][*]Hide the vector at the origin and the point [b]P’[/b]. [br][/*][*]Using the input bar enter: [b]Speed=Length[v][/b][br][/*][/list]
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4.2.

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5.

Tasks

  • 1. Suggested tasks

5.1.

Suggested tasks

Create GeoGebra worksheets that feature the use of CAS, Vectors and 3D views[br][br]Suggested ideas:[br][list][*]Factorised/expanded form of a cubic and its graph[br][/*][*]Relationship between functions and their derivatives/integrals[br][/*][*]Dynamic force diagrams with forces for vectors[br][/*][*]Vector equation of a line in 2D[br][/*][*]Vector/cartesian equation of a plane[br][/*][/list]
– GeoGebra Institute of MEI

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