1. 6.4 Vector and Dot Products

2. Dot Product  This vector product results in a scalar  Example 1: Find the dot product

3. Properties of dot products  Let u, v and w be vectors and let c be a scalar

4. Angle between two vectors  If θ is the angle between two non zero vectors u and v, then  Vectors u and v are orthogonal (perpendicular) if their dot product is 0 See page 460 Figure 6.32 for all the possible orientations of 2 vectors

5. Example 2: Find the angle between the vectors

6. Example 3: Determine whether u and v are orthogonal, parallel or neither

7. Finding Vector Components Let u and v be non zero vectors such that u = w 1 +w 2 where w 1 and w 2 are orthogonal and w 1 is parallel to v. The vector w 1 is the projection of u onto v and is denoted by w 1 =proj v u. w 2 =u – w 1

8. Work=(magnitude of force)(direction)  The work W done by a constant force F as its point of application moves along vector PQ is given by

9. Example 4: Find the projection of u onto v

10. Assignment  Page 464 #1-23odd, 33-41odd, 59