Vector Bus Tour

1. Vector Bus Tour

2. Bus Tour Warm Up 1 On a set of axes like those below Starting at (0,0) which points can you reach using only combinations of the two vectors below?

3. Bus Tour Warm Up 2 • Victor is delivering vegetables in his van.

4. C F H A E B G D

5. Write down any pathway Victor can take to get him from A to H For example, he could do this: or he could do this: C F H A E B G D A C F H A E D G H

6. Write down any pathway Victor can take to get him from A to H C F H A E B G D Write down the vectors of your pathway. Write down the vectors of some other pathways from A to H. What do you notice?

7. What is the vector if you travel from A to H directly? C F H A E B G D What do you notice?

8. What do the vectors associated with the pathway F H G B C F add up to? C F H A E B G D

9. Climb Aboard the Vector Bus!!! You have arrived on Vector Island!!! You and your band are gigging around the island and must visit all of the music venues. Each of you has one of the following vector bus passes. This determines which group you will be working in.

10. Vector Island

11. Climb Aboard the Vector Bus!!! • You must use your own bus pass at least once • on the journey. You can use vectors in either a • positive or negative direction. • Your route should be as follows: • Scalar Shipyard • Magnitude Museum • Notation Noise Arena • Direction Disco • Collinear Colosseum • Gradient Groove • Parallel Place • Vector Venue • Scalar Shipyard

12. Vector Bus Tour One Possible Set of Solutions is shown on the following slides

13. Possible solutions for the vector bus game • Journey 1: From Scalar Shipyard to Magnitude Museum • Vector a’s = 3b - 2a • Vector b’s= b - e • Vector c’s = d - c - e • Vector d’s = d - c - e • Vector e’s = b – e • Journey 2: From Magnitude Museum to Notation Noise Arena • Vector a’s = a + d + e • Vector b’s= 2b - d • Vector c’s = b + c + 2e • Vector d’s = 3d + 3e • Vector e’s = 3d + 3e

14. Possible solutions for the vector bus game • Journey 3: From Notation Noise Arena to Direction Disco • Vector a’s = 2a + 2e • Vector b’s= 4b - 4d • Vector c’s = 4a - b + c - d + 2e • Vector d’s = 4b - 4d • Vector e’s = 2a + 2e • Journey 4: From Direction Disco to Collinear Colosseum • Vector a’s = 2e - a • Vector b’s= b - c - d + 2e • Vector c’s = e - 2c • Vector d’s = b - c - d + 2e • Vector e’s = e - 2c

15. Possible solutions for the vector bus game • Journey 5: From Collinear Colosseum to Gradient Groove • Vector a’s = b - 2a + e • Vector b’s= -b - c • Vector c’s = -b - c • Vector d’s = e - d • Vector e’s = e - d • Journey 6: From Gradient Groove to Parallel Place • Vector a’s = c - 2a - 2e • Vector b’s= c + 4d - 4b • Vector c’s = c - 2a - 2e • Vector d’s = c + 4d - 4b • Vector e’s = c - 2a - 2e

16. Possible solutions for the vector bus game • Journey 7: From Parallel Place to Vector Venue • Vector a’s = -a - d • Vector b’s= c - b + 2e • Vector c’s = c - b + 2e • Vector d’s = -a - d • Vector e’s = e + d - 2b • Journey 8: From Vector Venue to Scalar Shipyard • Vector a’s = a - 2b - 5e • Vector b’s= a - 2b - 5e • Vector c’s = 2c - e • Vector d’s = 4d - 4a • Vector e’s = a - 2b - 5e