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1. Draw any quadrilateral Find the midpoints of each side Connect them in order… And you get a parallelogram This is always true no matter what quadrilateral you draw Geometric problems like this can be understood using vectors . Vectors are also used to understand physical situations, such as the motion of objects acted on by different forces, in an advanced field of maths: Mechanics .

2. Vectors Vectors are a way of describing movement They have both a magnitude (size) and a direction Eg ) Speed is not a vector as it only has a magnitude Velocity is a Vector as it will have a direction as well as magnitude

3. What is a Vector? B A A vector is often represented by a line with an arrow. One way to name this vector is to use: Another way is to call it or (bold is used in type, handwritten we underline) We must do this to show it is a vector NOT a line.      

4. Equal Vectors B A Two vectors are equal if they have the same MAGNITUDE (size) and DIRECTION . D C F E H G

5. Vectors A H G F E D C B I Which Vectors are equivalent to AB? BC, DE, EF, GH, HI Which Vectors are equivalent to CI? BH, AG Which Vectors are equivalent to GE? DB, EC, HF Which Vectors are equivalent to AF? DI

6. Vectors Vectors which are parallel will be represented by the same letter(s). If the distance is doubled, so is the quantity Vectors which are parallel but in the opposite direction are represented by the negative of the letter given a 2a 1 / 2 a -a -2a - 1 / 2 a

7. Vectors A H G F E D C B I 2 a If a = AB, what is DF? If b = BE, what is FC? If c = CI, what is DG? If d = DF, what is HG? - b ½ c - ½ c

8. Vectors Combining Vectors You can combine Vectors by addition or subtraction The order is not important, but it is important to note that the final Vector is a straight line, NOT the 2 separate Vectors together… a b a b a+b b a b+a

9. Vectors Combining Vectors You can combine Vectors by addition or subtraction The order is not important, but it is important to note that the final Vector is a straight line, NOT the 2 separate Vectors together… a -b a b a-b -b a - b+a

10. Vectors A H G F E D C B I Let a = AB and b = BE Example 5 Give in terms of and .   Your Turn 5 Give in terms of and .   Example 6 Give in terms of and .   Your Turn 6 Give in terms of and .  

11. Exercise

12. ANSWERS

13. Find as many other vectors as you can expressed in terms of and .  

14. Answers