Chapter 12 - Vectors And The Geometry Of Space

1. 12.3 - The Dot Product

1.1. Angle Between Vectors:

1.2. Dot Product:

1.3. Untitled

1.4. Perpendicular Vectors:

1.5. Dot Product Properties and Vector Projections

1.5.1. Dot product properties

1.5.2. Projection and component

1.6. Work:

2. 12.4 - The Cross Product

2.1. The Cross Product of Two Vectors in Space:

2.2. Parallel Vectors

2.3. Properties of Cross Products:

2.4. Area of Parallelogram:

2.5. Cross Product as a Determinant:

2.6. Torque:

2.7. Triple Scalar or Box Product:

3. 12.5 - Lines and Planes in Space

3.1. Parametric Equation for a Line:

3.2. Vector Equation for a Line:

3.3. The Distance from a Point to a Line in Space:

3.4. Angle Between Planes:

3.5. The Distance from a Point to a Plane:

3.6. Equation for a Plane in Space:

3.7. Lines of Intersection:

4. 12.1 - Three Dimensional Coordinate System

4.1. Distance

4.2. Sphere

5. 12.2 - Vectors

5.1. Magnitude or Length of a Vector:

5.2. Component Form:

5.3. Unit Vector

5.4. Vector Algebra Operations:

5.5. Mid-point of a Line Segment

6. Cylinders and Quadric Surfaces

6.1. Quadric Surfaces:

6.1.1. The Hyperbolic Paraboloid:

6.1.1.1. Hyperbolic Paraboloid Image

6.1.2. The Ellipsoid:

6.1.2.1. Ellipsoid Image

6.1.3. Elliptical Paraboloid:

6.1.3.1. Elliptical Paraboloid Image

6.1.4. Elliptical Cone:

6.1.4.1. Elliptical Cone Image

6.1.5. Hyperboloid of One Sheet:

6.1.5.1. Hyperboloid of One Sheet Image

6.1.6. Hyperboloid of Two Sheets:

6.1.6.1. Hyperboloid of Two Sheets

6.2. Cylinders: