1. 6.4 Vectors and Dot Products
Finding the angle between two vectors
Writing a vector as the sum of two vectors components

2. Definition of Dot Product
Given: Two vectors in Component form
The result is a number, not a vector

3. Find the Dot Product
Given

4. Find the Dot Product
Given

5. Products of the Dot Product

6. The Angle Between two vectors
For angles

7. The Angle Between two vectors
For angles
Find the angle between

10. The Angle Between two vectors
For angles
Vectors are Orthogonal if there
Dot Product (u●v)= 0
What is the angle between the vectors, Why?

11. Definition of Vector Components
Let u and v be nonzero vectors.
u = w1 + w2 and w1 · w2 = 0
Also, w1 is a scalar of v
The vector w1 is the projection of u onto v, So w1 = proj v u
w 2 = u – w 1

12. Decomposing of a Vector Using Vector Components

13. Decomposing of a Vector Using Vector Components

14. Decomposing of a Vector Using Vector Components

15. Definition of Work Work is force times distance.
If Force is a constant and not at an angle
If Force is at an angle

16. Homework
Page 447 – 448
# 1, 5, 17, 21, 25,
29, 33, 37, 41,
45, 49, 53, 63, 67

17. Homework
Page 447 – 448
# 4, 8, 12, 16,
20, 24, 28, 32,
36, 40, 52