# CEMC Geogebra Supplement

- Author:
- John Rodgers

This book contains supplementary materials to illustrate the content provided by the CEMC course Calculus and Vectors.

## Table of Contents

### Introduction to Vectors

### Algebraic Vectors and Applications

- Algebraic Vectors
- Vector Manipulative
- Scalar Multiplication
- Unit Vectors: Hat i
- Unit Vectors: Hat j
- The Projection of u onto v
- Cross Product
- Area of a Parallelogram and Cross Product
- Area of a Triangle Sample
- 3-d Co-ordinates
- Coordinates01
- Coordinates02
- Coordinates03
- Coordinates04
- Coordinates05
- How Long is a 3-D Hypotenuse?
- Direction Angles
- Unit Vectors in 3D
- Volume of a Parallelopiped

### Equations and Intersections of Lines in R2 and R3

### Equations and Intersections of Planes

- Parameteric Equations of the Plane
- Vector and Parametric Equations of the Plane
- Normal Vector and Plane
- Skew Lines to Parallel Planes
- Normal, a Plane, and a General Vector
- Distance Between Skew Lines
- Finding the Distance: Point to a Plane
- How Many Solutions I
- How Many Solutions II
- How Many Solutions III
- Planes, Normals and Intersections
- Planes and Intersections I
- Planes and Intersections II
- One Solution to Rule Them All
- No Solutions
- Linear Solution
- Pup Tent Solution
- Planes and Normals
- Two Solutions