VECTORS AND ANALYTIC GEOMETRY IN SPACE
CHAPTER 1: COORDINATES AND VECTORS IN SPACE
1. COORDINATES IN SPACE
A. BASIC CONCEPTS
1. The Three-Dimensional Coordinate System
2. The Distance Between Two Points
B. SPHERES
1. The Standard Equation of a Sphere
2. The General Equation of a Sphere
2. VECTORS IN SPACE
A. BASIC CONCEPTS
B. VECTOR OPERATIONS
1. Adding and Subtracting Vectors
2. Multiplying a Vector by a Scalar
3. Linear Combinations of Vectors
C. PARALLEL VECTORS
D. THE DOT PRODUCT
1. The Dot Product of Two Vectors
2. The Angle Between Two Vectors
3. Vector Projections
E. THE CROSS PRODUCT
1. Matrices and Determinants
2. The Cross Product of Two Vectors
Activity: Torque
CHAPTER 2: ANALYTIC GEOMETRY IN SPACE
1. LINES AND PLANES IN SPACE
A. LINES IN SPACE
1. The Equation of a Line in Space
2. The Equation of a Line through Two Points in Space
3. The Angle Between Two Lines
4. The Distance Between a Point and a Line
B. PLANES IN SPACE
1. The Equation of a Plane
2. The Angle Between Two Planes
3. Families of Planes
4. The Distance Between a Point and a Plane
2. SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES
A SYSTEMS OF TWO EQUATIONS
B. SYSTEMS OF THREE EQUATIONS
C. CRAMER’S RULE