1. 10.5 The Dot Product

4. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property

5. Theorem Angle between Vectors

8. Two vectors v and w are said to be parallel if there is a nonzero scalar  so that v =  w. In this case, the angle  between v and w is 0 or 

9. Determine whether the vectors v = -3i + 2j and w = -9i + 6j are parallel.

10. Theorem Two vectors u and v are orthogonal if and only if

11. Determine whether the vectors v = 4i - j and w = 2i + 8j are orthogonal.

13. Theorem

18. The work W done by a constant force F in moving an object from A to B is defined as

19. Find the work done by a force of 50 pounds acting in the direction 3i + j in moving an object 20 feet from (0, 0) to (20, 0).