1. 6.2 Dot Products of Vectors

2. I. Dot Products
A.) Def. - A scalar quantity representing the multiplication of two vectors used to calculate the angle between two vectors.

3. B.) Properties

4. C.) Ex. 1 – Find each dot product.

5. D.) Ex.2- Use the dot product to find the length of v.

6. II. Angles Between Vectors
A.) Thm: If θ is the angle between two non-zero vectors u and v, then
Proof is in the book. KNOW IT!!!

7. B.) Ex. 3 – Find the angle between vectors u and v.

8. C.) Vectors are perpendicular if
D.) Vectors are orthogonal iff
(Note: the zero vector is orthogonal to every vector in the plane, but not considered perpendicular.)

9. II. Vector Projection
A.) The projection of u = onto v = is the vector determined by dropping a perpendicular from Q to Q u P R S v

10. The notation for the projection of u onto v is given by the following:Q S R u
The notation for the projection of u onto v is given by the following:

11. B.) Def- The projection of u onto v if u and v are both non-zero vectors is

12. C.) Ex. 4 - Find the vector projection of u onto v if .

13. D.) Now, write u2 as the sum of two orthogonal vectors, one of which is the