Math 242, Fall 2013, Assignment 3

We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable mangitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.

- Voltaire

Carefully state the following definitions, then give one example and one non-example of each:

1. Vector equation (of a line).
2. Symmetric equations (of a line).
3. Vector equation (of a plane).
4. Scalar equation (of a plane).
5. Normal vector (to a plane).
6. Angle (between two planes).
7. Distance (between two planes).
8. Distance (between two lines).
9. Function of two variables.
10. Domain.
11. Range.
12. Graph.
13. Method of traces.
14. Cylindrical coordinates (of a point in space).
15. Spherical coordinates (of a point in space).

Solve the following problems:

1. Section 9.5, problems 5, 7, 21, 23, 25, 39, 53, and 55.
2. Section 9.6, problems 5, 11, 13, 15, 17, and 21.
3. Section 9.7, problems 3, 5, 7, 9, 15, 21, and 25.

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