# Math 221: Study Guide - Chapter 12

1. Describe the surface whose equation is given. Look at problems 12.1.13-18.
2. Find parametric equations for the lines described. Two parts. Look at problems 12.5.3-4, 11-18.
3. Find the angle between two vectors. Look at example 2 in 12.3.
4. Find the equation of the plane passing through the given point with the given normal vector. Look at problems 12.6.3-6.
5. Find the point of intersection of the line and the plane. Look at problems 12.6.17-18.
6. Find the distance between the point and the plane. Look at problems 12.6.39-40.
7. Convert from rectangular coordinates to cylindrical coordinates. Look at problems 12.8.1-2.
8. Convert between spherical coordinates and rectangular coordinates. Look at example 4 in 12.8.
9. Convert the equation from cylindrical coordiantes into rectangular coordinates. Look at problems 12.8.15-21.
10. Convert the equation from spherical coordinates into rectangular coordinates. Look at problems 12.8.23-30.
11. Find the volume of the parallelpiped with the given adjacent sides. Look at problems 12.4.21-22.
12. 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.
13. Identify, but do not sketch, the quadric surface. Six parts. Look at problems 12.7.11-22.
14. True or False. Know properties of vectors from sections 12.2 - 12.4. Many involve dot products, cross products, scalar triple products.
15. 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.
16. Sketch the three dimensional surface whose equation is given. Look at problems 12.1.25-34.
17. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total 4 8 4 4 4 4 4 4 4 4 4 3 6 13 18 4 8 100