Calculus III

Chris Mizell

Dynamic GeoGebra worksheets for Calculus III classes everywhere, but mostly in Niceville, Florida.

Table of Contents

  1. 11 Vectors and the Geometry of Space
    1. 11.1 The Associative Property of Vector Addition
    2. 11.2 3D Distance Formula
    3. 11.3 Vector Projections in the Plane
    4. Optimizing the Moment of a Force
    5. 11.4 Volume of a Parallelepiped
    6. 11.5 Line in Space
    7. 11.5 Plane in Space
    8. 11.5 Distance between a point and a plane
    9. 11.6 Quadric Surfaces
    10. 11.7 Rectangular, Cylindrical, and Spherical Coordinates
  2. 12 Vector-Valued Functions
    1. Helix Graph of a Vector-Valued Function
    2. Analyze the velocity and acceleration of a particle.
    3. Projectile Motion 3D
    4. Spherical Coordinates Target Practice
    5. Viviani's Curve - Velocity and Acceleration Vectors
    6. Interpreting Curvature

1.

11 Vectors and the Geometry of Space

  • 1. 11.1 The Associative Property of Vector Addition
  • 2. 11.2 3D Distance Formula
  • 3. 11.3 Vector Projections in the Plane
  • 4. Optimizing the Moment of a Force
  • 5. 11.4 Volume of a Parallelepiped
  • 6. 11.5 Line in Space
  • 7. 11.5 Plane in Space
  • 8. 11.5 Distance between a point and a plane
  • 9. 11.6 Quadric Surfaces
  • 10. 11.7 Rectangular, Cylindrical, and Spherical Coordinates

1.1.

11.1 The Associative Property of Vector Addition

Move the points at the heads of vectors u, v, and w to re-position them. Select either (u + v) + w or u + (v + w) to see that the vector sum is the same.
– Chris Mizell

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

2.

12 Vector-Valued Functions

  • 1. Helix Graph of a Vector-Valued Function
  • 2. Analyze the velocity and acceleration of a particle.
  • 3. Projectile Motion 3D
  • 4. Spherical Coordinates Target Practice
  • 5. Viviani's Curve - Velocity and Acceleration Vectors
  • 6. Interpreting Curvature

2.1.

Helix Graph of a Vector-Valued Function

Enter the 3 components of the vector-valued function as real-valued functions of t. Then start the graph.
– Chris Mizell

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

Information