Problem Set 1—3D Coordinates

Purpose

This problem set reinforces your understanding of 3-dimensional coordinate systems and of simple curves and surfaces in them.

Background

This problem set is based on material in sections 12.1 and 12.6 of our textbook. We will discuss section 12.1 in class on September 2, 12.6 on September 4, and material on muPad (the computer algebra system in Matlab) that is not in the text but is needed for the last two problems of this exercise on September 9.

Activity

Solve each of the following problems:

Problem 1

Exercise 6 in section 12.1 of our textbook (what is the shape of the set of points satisfying the equations x² + y² = 4 and z = -2).

Problem 2

Exercise 56 in section 12.1 of our textbook (what are the center and radius of the sphere defined by x² + y² + z² - 6y + 8z = 0).

Problem 3

Exercise 6 in section 12.6 of our textbook (identify the surface defined by x = -y² - z²).

Problem 4

Use muPad to solve exercise 54 in section 12.6 of our textbook (graph the surface defined by x²/9 - z²/9 = 1 - y²/16).

Problem 5

Use muPad to solve exercise 58 in section 12.6 of our textbook (graph the surface defined by y - √(4-z²) = 0).

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as that will speed the process along.

Sign up for a meeting via Google calendar. If you worked in a group on this exercise, the whole group should schedule a single meeting with me. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.