Math 221 - Chapter 14 Study Guide

1. Describe the surface whose equation is given. Look at problems 14.1.20-25*
2. Sketch the surface whose equation is given. Look at problems 14.1.32-39*
3. Find parametric equations for the line passing through two points, the line segment joining two points, and the line tangent to a circle at a given point. Look at problems 14.5.1-15, 19
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 14.6.1-4
6. Find the intersection of a line and a plane. Look at problem 14.6.10
7. Find the distance between a point and a plane. Look at problems 14.6.33-35
8. Name and sketch the quadric surface. Two parts. Look at problems 14.7.7-28*
9. Convert rectangular coordinates to cylindrical coordinates. Look at 14.8.1
10. Convert rectangular coordinates to spherical coordinates. Look at 14.8.39
11. Convert the equation in cylindrical coordinates into rectangular coordinates. Look at 14.8.7-14
12. Convert the equation in spherical coordinates into rectangular coordinates. Look at 14.8.15-22
13. Find the volume of the parallelepiped. Look at problem 14.4.25
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:

• Problems with an * are directly from the text. Where other problems are indicated, the problem on the test is similar to the problem in the text.