1. VECTORSVECTORS Describing paths

2. VECTOR: line segment with… i. Direction(an angle) ii. Magnitude||v|| = length of vector (distance)

3. EX: AB Point A is the origin or initial point Point B is the endpoint or terminal point A B

4. A B Basic terminology and notation: v Let v = A B ZERO VECTOR: ||v|| = 0

5. EQUAL VECTORS: Same magnitude & direction

6. Also Equal

7. NOT EQUAL

9. VECTOR SUM: XY + YZ = XZ X Y Z

10. Opposite vectors: v - w v w -w

11. Notationv = 3 right, 4 up from initial point

12. w = V =

13. EX 1: Graph 2v -3w

14. a b || V || = ? || v || = Magnitude or length

15. APPLICATION PROBLEMS Write a vectors representing the situation and draw the resulting trip. A small motorboat in still water maintains a speed of 10 mph. When the boat heads directly across a river it is perpendicular to the 4mph current. At what speed will the boat actually be travelling?

16. The Resultant Velocity is the sum of the two Velocities current boat

17. VECTOR ANGLE EXAMPLE: Sketch a vector 60 degrees North of East

18. THE DOT (scalar) PRODUCT v · w = a 1 a 2 + b 1 b 2 v = w =

19. EXAMPLES: FIND: v · w w · v v · v w · w v = w =