# Math 221: Chapter 12 Study Guide

1. Describe the surface whose equation is given. Look at problems 12.1.13-18
2. Sketch the surface whose equation is given. Look at problems 12.1.25-34
3. Find parametric equations for the line passing through two points and the line tangent to a circle at a given point. Look at problems 12.5.3-4, 11-20
4. Given two vectors, find a sum, scalar product, norm, dot product, cross product, projection of one vector onto another, unit vector. Also find the angle between the two vectors.
5. Find the equation of a plane passing through a given point with the given normal vector. Look at problems 12.6.3-6
6. Find the intersection of a line and a plane. Look at problem 12.6.17-18
7. Find the distance between a point and a plane. Look at problems 12.6.39-40
8. Name and sketch the quadric surface. Two parts. Look at problems 12.7.11-22
9. Convert rectangular coordinates to cylindrical coordinates. Look at 12.8.1-2
10. Convert rectangular coordinates to spherical coordinates. Look at 12.8.7-8
11. Convert the equation in cylindrical coordinates into rectangular coordinates. Look at 12.8.15-22
12. Convert the equation in spherical coordinates into rectangular coordinates. Look at 12.8.23-30
13. Find the volume of the parallelepiped. Look at problem 12.4.21-22
14. Identify each statement as true or false. If false, change the right hand side so the statement is true. Thirteen parts. These are statements about dot products, cross products, and norms of vectors.

## Notes:

• Many of the problems are directly from the text.