Class Group Exercise and Homework Assignment
(Due 1/18)

Instructions: Do as much of Part 1 as you can in your groups in class on Friday. Write up a NEAT set of answers (one per group) and turn them in Wednesday. For Part 2 you can still consult, but each student should write up and turn in an individual answer to each question.

Part 1. Practice basic tools (submit as a group)

A. Find the equation of a plane through 3 points:

1. Find the equation of the plane through the points
   A = (3, 2, 1), B = (2, 3, -1), C = (1, 0, 1).
2. Find the equation of the plane through the points E = (2, 1, 1), F = (5, 3, -1), G = (-2, 2, 0)

B. Find the equation of a plane perpendicular to a line:

1. Find the equation of the plane through the point P = (1, 2, 1) that is perpendicular to the line OG, where O = (0,0,0) and G = (1, 1, -1). Also, tell at what point the plane intersects line OG.

2. Find the equation of the plane through point Q = (3, 4, 5) that is perpendicular to line OQ, where O = (0,0,0).

3. Find the equation of the plane through O = (0,0,0) that is perpendicular to the line AB, where A = (1, 2, 3) and B = (3, 2, 1).

C. Find the intersection of a line and a plane:

1. Find where the line AB intersects the plane whose equation is x – y + 2z = 0, where A and B are as in B3 above.

2. Find where the line AB intersects the plane whose equation is x + y + z = 6, where A and B are as in B3 above.

3. Find where the line AB intersects the plane whose equation is 2x + 3 y + 2z = 0, where A and B are as in B3 above.

D. Find parallel lines and planes:

1. Write down a parameterization for the line AB, where A and B are as in B3.

2. Find the equation of a plane parallel to both line AB and line OC, where O = (0,0,0) and C = (1, 1, 1).