1. Sections 8-4 and 8-5
Vectors

2. Vocabulary
1. Vector – a quantity that has both magnitude and direction.
2. Magnitude – the length of the line segment.
3. Direction – the directed angle between the positive x axis and the vector.

3. 4. Resultant – the sum of two or more vectors
5. Unit vector – a vector with magnitude of one unit
Inner product of vectors in a plane-
7. Inner product of vectors in space -

4. 8. Perpendicular vectors – vectors with an inner product of zero.
9. Parallel vectors – vectors with the same direction and different magnitude
10. Standard position – vectors with an initial point at the origin

5. Inner Product

6. (10,4)

8. 2, not perpendicular
13, not perpendicular
5, not perpendicular

9. Geometric Vectors Sum of two vectors Parallelogram Method

10. Geometric Vectors Sum of two vectors Triangle Method

12. Triangle Method

15. One clown is exerting a force of 270 and the other is 360
One clown is exerting a force of 270 and the other is 360. (Use the parallelogram method.)
Clown 1
Bull Clown 2

16. Determine the resultant forces.

17. Example 1, page 514

18. Lenny Montana was a former 5-year world heavy weight wrestling champion and actor. Suppose that Lenny and a tag team wrestling partner are each pulling horizontally and at a rt angle to each other on the arms of a wrestling opponent. Lenny exerts a force of 180 pounds due north while his partner exerts a force of 125 pounds due east.

19. Draw a labeled diagram that represents the forces.

20. Determine the resultant force exerted on the opponent.
219 lb
Determine the angle the resultant force makes with the east-west axis.
55.2° north of east

23. Find the magnitude and the direction for the resultant vector

24. Find the magnitude and the direction for the resultant vector

25. Textbook page 509 # and
Textbook page 517 # 4,5,6 and #10-#15

26. Example 2, pg 514
Alvaro works for a package delivery service. Suppose he is pushing a cart full of packages weighing 100 pounds up a ramp 8 feet long at an incline of 25°. Find the work done by gravity as the cart moves the length of the ramp. Assume that friction is not a factor.

27. Diagram 8

29. Apply the formula for work done by gravity

30. Justin works for a package delivery service
Justin works for a package delivery service. Suppose that he is pushing a cart full of packages weighing 125 pounds up a ramp 10 feet long at an incline of 20°. Find the work done by gravity as the cart moves the length of the ramp. Assume that friction is not a factor.
ft-lb