1. Dot Product of Vectors

2. Definition of Dot Product
Given: Two vectors in Component form

3. Example: Find the Dot Product

4. Dot PRODUCT The result is not a vector.
It is a real number, that is, a scalar.
For this reason, the dot product is sometimes called the scalar product (or inner product).

5. Properties of the Dot Product
Let u, v, and w be vectors in the plane or in space and let c be a
scalar.

6. DOT PRODUCT— Alternative-DEFINITION
If is the angle between the vectors a and b, then

7. If is the angle between the nonzero vectors a and b, then

8. Example:

9. Orthogonal Vectors
Perpendicular orthogonal What will be the dot product of two orthogonal vectors?

10. A use of the dot product is found in the formula below:
The work W done by a constant force F in moving an object from A to B is defined as
This means the force is in some direction given by the vector F but the line of motion of the object is along a vector from A to B

11. Class-work

12. Home work Page-586+ Quick review exercise 1-5, 7, 10
Section 12.2 exercise
7, 36
14 (optional)