# Math 221: Study Guide - Chapter 12

- Describe the surface whose equation is given. Look at problems 12.1.13-18.
- Find parametric equations for the lines described. Two parts. Look at problems
12.5.3-4, 11-18.
- Find the angle between two vectors. Look at example 2 in 12.3.
- Find the equation of the plane passing through the given point with the
given normal vector. Look at problems 12.6.3-6.
- Find the point of intersection of the line and the plane. Look at problems
12.6.17-18.
- Find the distance between the point and the plane. Look at problems 12.6.39-40.
- Convert from rectangular coordinates to cylindrical coordinates. Look at
problems 12.8.1-2.
- Convert between spherical coordinates and rectangular coordinates. Look
at example 4 in 12.8.
- Convert the equation from cylindrical coordiantes into rectangular coordinates.
Look at problems 12.8.15-21.
- Convert the equation from spherical coordinates into rectangular coordinates.
Look at problems 12.8.23-30.
- Find the volume of the parallelpiped with the given adjacent sides. Look
at problems 12.4.21-22.
- Identify whether the trace of the surface in the given place is a circle,
ellipse, parabola, or hyperbola. Three parts. Look at problems 12.7.9-10.
- Identify, but do not sketch, the quadric surface. Six parts. Look at problems
12.7.11-22.
- True or False. Know properties of vectors from sections 12.2 - 12.4. Many
involve dot products, cross products, scalar triple products.
- Given three vectors, simplify the expressions. These could involve sums,
scalar products, norms, dot products, cross products, projections, scalar
triple products, finding unit vectors, and vectors parallel to a given vector.
- Sketch the three dimensional surface whose equation is given. Look at problems
12.1.25-34.
- Identify and sketch the quadric surface. Two parts. Look at problems 12.7.11-22.

## Notes

- Questions 15 - 17 must be worked without a calculator or computer.
- You may use the technology exercise on Quadric surfaces that you prepare
for this chapter on the test.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
Total |

Pts |
4 |
8 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
3 |
6 |
13 |
18 |
4 |
8 |
100 |