1. 8.1 Geometric Vectors Use the worksheet vectors for Assignment #58
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.

2. By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
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3. Some info about vectors
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Some info about vectors
Mathematical representation of magnitude (size) and direction.
Standard position: A vector whose initial point is at the origin
Resultant Vector: A vector that is the sum of two or more vectors.

4. Resultant Vectors 𝑎 + 𝑏 = 𝑐 𝑎 +2 𝑏 = 𝑐
terminal point
Resultant Vectors
Initial point 𝑏 𝑎
terminal point
Initial point
Parallelogram Method
Match up initial points…make a parallelogram
Triangle Method
Match up initial point to terminal point…make a triangle
𝑎 + 𝑏 = 𝑐
𝑎 +2 𝑏 = 𝑐
− 𝑏 means switch the initial and terminal point 𝑏
− 𝑏

5. Example 1: Using either method, draw the resultant vector
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 1: Using either method, draw the resultant vector 𝑎 2 −2
− 𝑎 𝑐 𝑏 −1 4 4 𝑑 3 −3 −1
𝑎 + 𝑏 −1 4

6. Example 1: Using either method, draw the resultant vector
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 1: Using either method, draw the resultant vector 𝑎
− 𝑎 𝑐 𝑏 𝑑
𝑏 − 𝑎

7. Example 1: Using either method, draw the resultant vector
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 1: Using either method, draw the resultant vector 𝑎
− 𝑎 𝑐 𝑏 𝑑
𝑏 −2 𝑑

8. Example 1: Using either method, draw the resultant vector
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 1: Using either method, draw the resultant vector 𝑎
− 𝑎 𝑐 𝑏 𝑑
2 𝑐 − 𝑏

9. By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 2: Write the geometric representation of the vectors as a sum/difference 𝑎
− 𝑎 𝑐 𝑏 𝑑
𝑎 +2 𝑏
2 𝑑 − 𝑎

10. By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Example 2: Write the geometric representation of the vectors as a sum/difference 𝑎
− 𝑎 𝑐 𝑏 𝑑
2 𝑏 +4 𝑑
2 𝑐 −2 𝑎

11. Summary 1. Sketch 2 𝑎 + 𝑏 𝑎 − 𝑎 𝑐 𝑏 𝑑
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Summary 𝑎
− 𝑎 𝑐 𝑏 𝑑
1. Sketch 2 𝑎 + 𝑏
2. Write the vector represented by the diagram.

12. Summary 1. Sketch 2 𝑎 + 𝑏 𝑎 + 𝑐 + 𝑏 𝑎 − 𝑎 𝑐 𝑏 𝑑
By the end of the period students will be able to add and subtract vectors geometrically as evidenced by a partner activity.
Summary 𝑎
− 𝑎 𝑐 𝑏 𝑑
1. Sketch 2 𝑎 + 𝑏
2. Write the vector represented by the diagram.
𝑎 + 𝑐 + 𝑏