1. 11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j

2. HW Review

3. Dot Product The dot product of two vectors of two vectors v = and w = is the scalar defined by:

4. Properties of the Dot Product

5. Dot Product and Angle Let θ be the angle between two non zero vectors v and w. Then or

6. Ex Find the angle between v = and w =

7. Orthogonal Vectors Two nonzero vectors are called perpendicular or orthogonal if the angle between them is π/2 or if = 0

8. Ex Determine whether v = is orthogonal to u = or w =

9. Obtuse Angles The angle between two vectors is obtuse if the dot product is < 0

10. Ex Determine whether the angles between vector v = and the vectors u = and w = are obtuse

11. Projection The projection of u along a nonzero v is the vector: OR

12. Ex Find the projection of u = along v =

13. Ex Find the decomposition of u = with respect to v =

14. Closure Find the projection of u = along v = HW: p.658 #3 4 5 7 9 11 15 21 23 25 29