11 Vectors
1. 11.4 3D Vectors
1. Section 11.4 Example 2
2. Section 11.4 Example 5
3. Section 11.4 Example 6
2. 11.5 Parallel and Unit Vectors
1. Section 11.5 Example 4
2. Section 11.5 Example 5
3. Section 11.5 Example 6
4. Section 11.5 Example 11
3. 11.6 The Scalar/Dot Product
1. Scalar/Dot Product Exploration
2. Section 11.6 Example 6
3. Section 11.6 Example 7
4. Section 11.6 Example 8
5. Section 11.6 Example 9
4. 11.7 The Vector Cross Product
1. Cross Product: Introduction
2. Scalar and Vector Projection
3. Section 11.7 Example 2
4. Section 11.7 Example 4
5. Geometric Interpretation of the Cross Product
6. Section 11.7 Example 5
7. Copy of Cavalieri's Principle
8. Section 11.7 Example 6
9. Section 11.7 Example 7
5. 11.8 Vector Applications to Geometry
1. Section 11.8 Example 1
2. Section 11.8 Example 2
3. Section 11.8 Example 3
4. Section 11.8 Example 4

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11 Vectors

Anthony Panontin, Nov 10, 2020

Algebraic Properties of Vectors

11.4 3D Vectors
1. Section 11.4 Example 2
2. Section 11.4 Example 5
3. Section 11.4 Example 6
11.5 Parallel and Unit Vectors
1. Section 11.5 Example 4
2. Section 11.5 Example 5
3. Section 11.5 Example 6
4. Section 11.5 Example 11
11.6 The Scalar/Dot Product
1. Scalar/Dot Product Exploration
2. Section 11.6 Example 6
3. Section 11.6 Example 7
4. Section 11.6 Example 8
5. Section 11.6 Example 9
11.7 The Vector Cross Product
1. Cross Product: Introduction
2. Scalar and Vector Projection
3. Section 11.7 Example 2
4. Section 11.7 Example 4
5. Geometric Interpretation of the Cross Product
6. Section 11.7 Example 5
7. Copy of Cavalieri's Principle
8. Section 11.7 Example 6
9. Section 11.7 Example 7
11.8 Vector Applications to Geometry
1. Section 11.8 Example 1
2. Section 11.8 Example 2
3. Section 11.8 Example 3
4. Section 11.8 Example 4

11.4 3D Vectors

1. Section 11.4 Example 2
2. Section 11.4 Example 5
3. Section 11.4 Example 6

Section 11.4 Example 2

Given vectors u and v, find: a) u + v, b) u - v, c) 2u and d) 3u - 4v

11.5 Parallel and Unit Vectors

1. Section 11.5 Example 4
2. Section 11.5 Example 5
3. Section 11.5 Example 6
4. Section 11.5 Example 11

Section 11.5 Example 4

a) Show that the vectors AB and BC are parallel. b) Find the midpoint of vector AB

11.6 The Scalar/Dot Product

1. Scalar/Dot Product Exploration
2. Section 11.6 Example 6
3. Section 11.6 Example 7
4. Section 11.6 Example 8
5. Section 11.6 Example 9

Scalar/Dot Product Exploration

1. Move the endpoints of the vectors. 2. Observe the value of the scalar/dot product. 3. What relationship(s) can you see between the vectors and the scalar/dot product?

11.7 The Vector Cross Product

1. Cross Product: Introduction
2. Scalar and Vector Projection
3. Section 11.7 Example 2
4. Section 11.7 Example 4
5. Geometric Interpretation of the Cross Product
6. Section 11.7 Example 5
7. Copy of Cavalieri's Principle
8. Section 11.7 Example 6
9. Section 11.7 Example 7

Cross Product: Introduction

[b][color=#980000]The cross product [/color][/b]of any 2 vectors [b]u[/b] and [b]v[/b] is yet [b][color=#980000]ANOTHER VECTOR! [/color][/b][br][br]In the applet below, vectors [b]u [/b]and[b] v[/b] are drawn with the same initial point. [br][br]The [b][color=#980000]CROSS PRODUCT[/color][/b] of u and v is also shown [b][color=#980000](in brown)[/color][/b] and is drawn with the same initial point as the other two. [br][br]Interact with this applet for a few minutes by moving the[b][color=#bf9000] initial point[/color][/b] and [b][color=#bf9000]terminal points[/color][/b] of both vectors around. [br][br]Then, answer the questions that follow.

1.

Use GeoGebra to measure the angle at which the line containing [b]u[/b] intersects the line containing the [b][color=#980000]cross product [/color][/b]vector. What do you get?

2.

Use GeoGebra to measure the angle at which the line containing [b]v[/b] intersects the line containing the [b][color=#980000]cross product [/color][/b]vector. What do you get?

3.

Given your responses for (1) and (2) above, what can we conclude about the [b][color=#980000]cross product[/color][/b] of any two vectors with respect to both individual vectors themselves?

4.

Is it possible to position vectors [b]u[/b] and [b]v[/b] so that their [b][color=#980000]cross product = the zero vector[/color][/b]? If so, how would these 2 vectors be positioned?

5.

How would vectors [b]u [/b]and [b]v[/b] have to be positioned in order for their [b][color=#980000]cross product[/color][/b] to have the greatest magnitude? Use GeoGebra to help informally support your conclusion(s).

11.8 Vector Applications to Geometry

1. Section 11.8 Example 1
2. Section 11.8 Example 2
3. Section 11.8 Example 3
4. Section 11.8 Example 4

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