1. Vectors Readings: Chapter 3

2. Vectors Vectors are the objects which are characterized by two parameters: magnitude (length) direction These vectors are equal Vectors can be considered as a set of two points in some space: Point A is an initial point (starting position) and Point B is a final point (ending position)

3. Vectors: example Vector: displacement of a car: initial point A, final point B Vector: velocity of a car, direction is the direction of the motion The speed of the car could be the same (the magnitude of velocity could be the same) but the directions of the motion will be different - different vectors - velocity.

4. Vectors Vectors are characterized by two parameters: length (magnitude) direction These vectors are the same

5. Sum of two vectors Sum of two vectors: Sum of two vectors: net displacement

6. Sum of vectors Sum of vectors: for many vectors the procedure is straightforward

7. Vectors: multiplication by number Vector (where is the positive number) has the same direction as, but its magnitude is times larger Vector (where is the negative number) has the direction opposite to, and times larger length

8. Vectors: multiplication by number

9. Vectors: Examples The magnitude of is 5 What is the direction and the magnitude of The magnitude of is, the direction is opposite to

10. Vectors: coordinate system and vector component coordinate system: (origin) Position of point A is characterized by 2 numbers

11. Vectors: coordinate system and vector components coordinate system: (origin) Vector is characterized by two numbers The meaning of this is the following: - vectors with unit magnitude

12. Vectors: coordinate system and vector components Then the sum of the vectors is the sum of their components: Magnitude of the vector: Direction of the vector:

13. Vectors: Example Find the magnitude and direction of the sum of three vectors with components (5,2) (-1,4) and (0,-2) Magnitude Direction Components of vector