1. Newton’s first law is only qualitative: we can’t use it calculate anything.
定性的

2. To go further, we need mathematical tools to describe motion:
3D vectors 矢量

3. 3D coordinate system
“Right-handed”
坐标系

4. A 3D vector is three numbers.
Remember units!
These are called the vector’s components.
Blackboard

5. SI units [Length] [Mass] [Time] meters kilograms seconds m kg s
Don’t forget to convert units!

6. A vector has a magnitude and a direction.

7. Magnitude: length of a vectorIf
, then
Magnitude is a scalar – just a number. 标量

8. Vectors can be made longer or shorter by multiplying with a scalar
Vectors can be made longer or shorter by multiplying with a scalar. The direction will be reversed if the scalar is negative. The angle of the vector does not change.

9. Direction: the unit vector
A unit vector has a magnitude of one, a points in some direction.
How to calculate the unit vector in the direction of another vector: If
, then
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10. Three special unit vectors
is the unit vector along the x axis
is the unit vector along the y axis
is the unit vector along the z axis

11. Three special unit vectors
Any vector can be written as a combination of these three unit vectors.
Example:

12. Two vectors are equal if they have the same magnitude and direction.

13. Which of these vectors is equal to <-4,2,0>?b c d e

14. Vector addition 加法

15. Vector addition y x

16. Vector addition y x

17. Vector addition y x

18. Vector subtraction 减法

19. Vector subtraction y x

20. Vector subtraction y x

21. Vector subtraction y x

22. Which of the following statements are correct?

23. “final position - initial position”
Displacement vectors 位移
A change in position, from position 1 to position 2, is given by:
Greek letter “Delta”
“final position - initial position”

24. Displacement vectors
Example: A snail is initially at location r1 = <3,0,-7> m. Later the snail has crawled to r2 = <2,0,-8> m. What is Δr, the change in the snail’s position?