Vector Multiplication and Applications

GROUP MEMBERS:

1. _____________________________

2. ______________________________

3. ______________________________

4. ______________________________

Have each group member sign the sheet.

Directions: Group faces towards one another. One person works at a time . Explain to the group what you are doing. If you need help, ask the people in your group for advice. Write out your work and answer on the sheet. When done, ask whether everyone in the group understands. People in the group ask questions. Pass the sheet to person 2 who will follow the same procedure. Then person 3 and so on.

P = (1, 2,3), Q = (-1, 1, 0), R = (2, 1, 1).

Part I: Vectors between points:

Person 1: Find the vector PR that goes from the point P to the point R. Explain what you are doing to your group. Does everyone understand?

 

 

 

 

 

 

  

 

Person 2: Find the vector PQ that goes from the point P to the point Q. Explain what you are doing to your group. Does everyone understand?

 

 

 

 

 

 

 

 

 

Person 3: Find the vector QR that goes from the point Q to the point R. Explain what you are doing to your group. Does everyone understand?

 

 

 

 

 

 

Person 3: Find the vector RQ that goes from the point R to the point Q. Explain what you are doing to your group. Does everyone understand? What is the relation between RQ and QR?

 

 

 

 

 

Part II: Equation of plane using the normal vector

 

Everybody: write the equation of the plane with normal n=(3, 2, -4) that goes through the

point P0= (5, -2, 7).

When everyone has figured out their answer, Person 4 write down her answer and check that it agrees with what other people got.

Person 1: The equation of the plane with normal n=(3, 2, -4) that goes through the point P0= (5, -2, 7) is

 

 

 

 

 

 

Everyone figure out the normal vector to the plane 3x - 7y + 4 z = 7

 

 

When everyone has figured out their answer, Person 1 write down her answer and check that it agrees with what other people got.

Person 2: The normal vector to the plane 3x - 7y + 4 z = 7 is n =

 

 

 

 

 

 

Group Discussion: Does the point (4, 1, -2) lie in the plane 3x - 7y + 4 z = -7?

 

Person 3: Write down your groups answer and justification.

 

 

 

 

 

 

 

Group Discussion: Does the point (4, 1, -3) lie in the plane 3x - 7y + 4 z = -7?

 

Person 4: Write down your groups answer and justification.