Vector Multiplication and Applications
GROUP MEMBERS:
1. _____________________________
2. ______________________________
3. ______________________________
4. ______________________________
Have each group member sign the sheet. Then introduce yourself to the group. Tell people: your name, where you are from, year, major, dorm, something fun you did this summer.
Problem: To find the normal vector to a plane generated by three points:
P = (1, 2,3), Q = (-1, 1, 0), R = (2, 1, 1).
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.Part I: Vectors between points:
Person 1: Find the vector PR that goes from the point P to the point R.
Then everyone working individually find the vector PQ that goes from the point P to the point Q.
Person 2: When everyone has finished their individual calculations of PQ, write down your answer here and see if everyone else in your group agrees with your answer.
Person 3: Find the vector QR that goes from the point Q to the point R.
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 4: 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 1: 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 2: 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 2: Write down your groups answer and justification.
Part III: Equation of Plane through 3 Points
Problem: To find the normal vector to a plane generated by three points:
P = (1, 2,3), Q = (-1, 1, 0), R = (2, 1, 1).
Each person take 2 vectors that lie in the plane from among the vectors PQ, PR, QR, QP, RP, RQ and then using these 2 vectors, calculate the normal to the plane. (see Part I). Then each person record their normal vector.
Person 3: n =
Person 4: n =
Person 1: n =
Person 2: n =
Discussion: Did you all get the same normal vector? If not, can you explain how there can be more than one correct answer to a math problem?
Given the normal vector you have calculated, each person calculate the equation of the plane and then record your answers. Again you might get different looking answers.
Person 3:
Person 4:
Person 1:
Person 2: