Vector Bus Tour

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

Bus Tour Warm Up 2

Victor is delivering vegetables in his van.

C F

B

A

D

E

H

G

Write down any pathway Victor can take to get him from A to H

C F

B

A

D

E

H

G

For example, he could do this:

A C F HA C F H

or he could do this:

A E D G HA E D G H

Write down any pathway Victor can take to get him from A to H

C F

B

A

D

E

H

G

Write down the vectors of your pathway.Write down the vectors of some other pathways from A to H.

What do you notice?

C F

B

A

D

E

H

G

What is the vector if you travel from A to H directly?

What do you notice?

C F

B

A

D

E

H

G

What do the vectors associated with the pathway

F H G B C F add up to?

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.

Vector Island

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:1.Scalar Shipyard2.Magnitude Museum3.Notation Noise Arena4.Direction Disco5.Collinear Colosseum6.Gradient Groove7.Parallel Place8.Vector Venue9.Scalar Shipyard

Vector Bus Tour

One Possible Set of Solutions is shown on the following slides

Possible solutions for the vector bus gameJourney 1: From Scalar Shipyard to Magnitude Museum

Vector a’s = 3b - 2aVector b’s = b - eVector c’s = d - c - eVector d’s = d - c - eVector e’s = b – e

Journey 2: From Magnitude Museum to Notation Noise Arena Vector a’s = a + d + eVector b’s = 2b - dVector c’s = b + c + 2eVector d’s = 3d + 3eVector e’s = 3d + 3e

Possible solutions for the vector bus gameJourney 3: From Notation Noise Arena to Direction Disco Vector a’s = 2a + 2eVector b’s = 4b - 4dVector c’s = 4a - b + c - d + 2eVector d’s = 4b - 4dVector e’s = 2a + 2e Journey 4: From Direction Disco to Collinear Colosseum Vector a’s = 2e - aVector b’s = b - c - d + 2eVector c’s = e - 2cVector d’s = b - c - d + 2eVector e’s = e - 2c

Possible solutions for the vector bus gameJourney 5: From Collinear Colosseum to Gradient Groove Vector a’s = b - 2a + eVector b’s = -b - cVector c’s = -b - cVector d’s = e - dVector e’s = e - d Journey 6: From Gradient Groove to Parallel Place Vector a’s = c - 2a - 2eVector b’s = c + 4d - 4bVector c’s = c - 2a - 2eVector d’s = c + 4d - 4bVector e’s = c - 2a - 2e

Possible solutions for the vector bus gameJourney 7: From Parallel Place to Vector Venue Vector a’s = -a - dVector b’s = c - b + 2eVector c’s = c - b + 2eVector d’s = -a - dVector e’s = e + d - 2b Journey 8: From Vector Venue to Scalar Shipyard Vector a’s = a - 2b - 5eVector b’s = a - 2b - 5eVector c’s = 2c - eVector d’s = 4d - 4aVector e’s = a - 2b - 5e