1. Dot Product of Vectors Today’s Objective: I can calculate the dot product and projections of vectors.

2. Quick Review

3. Multiplying Vectors Cross Product vector product or outer product Results in a vector perpendicular to the plane of the two vectors (3 rd dimension) Not in this unit. Proof of Property 1:

4. Find each Dot Product

5. Angle between Vectors

6. What is the dot product of vectors u and v, if they are perpendicular? The vectors u and v are orthogonal if and only if u·v = 0. Orthogonal means perpendicular. Pg. 472 #1-6, 15-20 Yes

7. Dot Product of Vectors Day 2 Today’s Objective: I can calculate the dot product and projections of vectors.

8. Pg. 470

9. Vector Projection Write u as the sum of two orthogonal vectors.

10. If u is a force, then proj v u represents the effective force in the direction of v. Juan is sitting on a sled on the side of hill inclined at 45°. The combined weight of Juan and the sled is 140 pounds. What force is required to keep the sled from sliding down the hill? Side of Hill vector: v = Force due to gravity: F = Force to keep from sliding: F 1 =proj v F Pg. 472 #24-26, 31-38, 45, 47