1. Lesson 3.1 Introduction to Vectors
Essential Question: How do you perform operations on vectors?

2. A student walks north from his house to his friend’s house
A student walks north from his house to his friend’s house. Then they both walk east to school. How would you describe their motion?

3. How do you describe motion in two dimensions?
Motion in two-dimensions is described using vectors.

4. What is a vector?
A physical quantity that has both direction and magnitude
Displacement
Velocity
Acceleration

5. What is a scalar? A quantity that has magnitude but no direction Speed
Volume
Number of pages in a book

6. When reading a textbook vectors are typically represented by boldface symbols or by drawing an arrow above the abbreviation for a quantity
𝐯 𝑣

7. One way to keep track of vectors and their directions is to use diagrams.
The vectors are shown as arrows that point in the direction of the vector.

8. What if you want to add vectors?
When adding vectors, you need to verify they have the same units and describe similar quantities.

9. What is a resultant vector?
A vector that represents the sum of two or more vectors

10. How can you find a resultant displacement?
You can add the vectors graphically
This approach is time consuming, and the accuracy of the answer depends on how carefully the diagram is drawn and measured.

11. A student walks from his house to his friend’s house, then from his house to the school. The student’s resultant displacement can be found by using a ruler and a protractor.

12. What are some properties of vectors?
Vectors can be moved parallel to themselves in a diagram.
Vectors can be added in any order.
To subtract a vector, add its opposite.
Multiplying or dividing vectors by scalars results in vectors.

13. Vectors can be moved parallel to themselves in a diagram
You can draw one vector with its tail starting at the tip of the other as long as the size and direction of each vector do not change.
The resultant vector can be drawn from the tail of the first vector to the tip of the last vector. This is the triangle method of addition.

14. Imagine looking down from the second level of an airport at a toy car moving at 0.80 m/s across a walkway that moves at 1.5 m/s. How can you determine what the car’s resultant velocity will look like from your view point?

15. Vectors can be added in any order
When two or more vectors are added, the sum is independent of the order of the addition.
The vector sum of two or more vectors is the same regardless of the order in which the vectors are added, provided that the magnitude and direction of each vector remain the same.

17. To subtract a vector, add its opposite.
Vector subtraction makes use of the definition of the negative of a vector.
The negative of a vector is defined as a vector with the same magnitude as the original vector but opposite in direction.

18. Multiplying or dividing vectors by scalars results in vectors
A vector multiplied by a scalar is still a vector.
A cab driver driving twice as fast as the original velocity vector is simply multiplied by 2
v cab ×2=2 v cab

19. How do you perform operations on vectors?