
# 12: Vectors and the Geometry of Space


• 12.7E: Exercises for Cylindrical and Spherical Coordinates
• Chapter 11 Review Exercises
• Cylindrical and Spherical Coordinates
The Cartesian coordinate system provides a straightforward way to describe the location of points in space. Some surfaces, however, can be difficult to model with equations based on the Cartesian system. As the name suggests, cylindrical coordinates are useful for dealing with problems involving cylinders. Similarly, spherical coordinates are useful for dealing with problems involving spheres.
• Equations of Lines and Planes in Space
To write an equation for a line, we must know two points on the line, or we must know the direction of the line and at least one point through which the line passes. In two dimensions, we use the concept of slope to describe the orientation, or direction, of a line. In three dimensions, we describe the direction of a line using a vector parallel to the line. In this section, we examine how to use equations to describe lines and planes in space.
• Exercises for Equations of Lines and Planes in Space
• Exercises for The Cross Product
• Exercises for The Dot Product
• Exercises for Vectors in Space
• Exercises for Vectors in the Plane