1. The Dot Product

2. http://ed.ted.com/on/yNkfx3wp

4. Given A(1, 2, 3), B(-2, 0, 3) and C(2, 5, -1), find A●B A. 2 B. 5.1 C. (2,3,6) D. 7

5. Given A(1, 2, 3), B(-2, 0, 3) and C(2, 5, -1), find A●B A. 2 B. 5.1 C. (2,3,6) D. 7

6. Given A(1, 2, 3), B(-2, 0, 3) and C(2, 5, -1), find C●B A. -5 B. 2.3 C. 4 D. (1,2)

7. Given A(1, 2, 3), B(-2, 0, 3) and C(2, 5, -1), find C●B A. -5 B. 2.3 C. 4 D. (1,2)

8. Find the angle between the vectors a = (2,1) and b = (3, 6) A. 100° B. 32° C. 37° D. 117°

9. Find the angle between the vectors a = (2,1) and b = (3, 6) A. 100° B. 32° C. 37° D. 117°

10. Find the angle between the vectors a = (2,1, 5 ) and b = (-3, 0, 4) A. 102° B. 18° C. 3° D. 59°

11. Find the angle between the vectors a = (2,1, 5 ) and b = (-3, 0, 4) A. 102° B. 18° C. 3° D. 59°

12. What is the dot product of two perpendicular vectors? A. 1 B. 0 C. 100 D. infinity

13. What is the dot product of two perpendicular vectors? A. 1 B. 0 C. 100 D. infinity

16. One important use of dot products is in projections. The scalar projection of b onto a is the length of the segment AB shown in the figure below.

17. The vector projection of b onto a is the vector with this length that begins at the intersection of a and b and is in the same direction (or opposite direction if the scalar projection is negative) as a.

18. Thus, mathematically, the scalar projection of b onto a is proj a b = |b|cos() (where is the angle between a and b)

21. Students will investigate the properties of projections and how they relate to the dot product. They will measure the shadow of a drinking straw and compare the length of the shadow (projection) to the angle between the straw and the normal. Students will be put into groups of three and given the following materials: 1 protractor 1 ruler 1 sheet of blank paper 1 drinking straw 1 flashlight The activity will be demoed by the teacher, and the groups will be given a worksheet to complete.