Introduction to Vectors

This workbook is designed to be used in conjunction with the author’s free online video tutorials. Inside this workbook each chapter is divided into learning modules (subsections), each having its own dedicated video tutorial.

View the online video via the hyperlink located at the top of the page of each learning module, with workbook and paper or tablet at the ready. Or click on the Introduction to Vectors playlist where all the videos for the workbook are located in chronological order:

Introduction to Vectors

http://www.YouTube.com/playlist?list=PLGCj8f6sgswnm7f0QbRxA6h4P0d1DSD6Q.

While watching each video, fill in the spaces provided after each example in the workbook and annotate to the associated text.

You can also access the above via the author’s YouTube channel

Dr Chris Tisdell’s YouTube Channel

http://www.YouTube.com/DrChrisTisdell

There has been an explosion in books that connect text with video since the author’s pioneering work Engineering Mathematics: YouTube Workbook [31]. The current text takes innovation in learning to a new level, with all of the video presentations herein streamed live online, giving the classes a live, dynamic and fun feeling.

1. The basics of vectors
   1. Geometry of vectors
   2. But, what is a vector?
   3. How big are vectors?
   4. Determine the vector from one point to another point
   5. Vectors in Three Dimensions
   6. Parallel vectors and collinear points example
   7. Vectors and collinear points example
   8. Determine the point that lies on vector: an example
2. Lines and vectors
   1. Lines and vectors
   2. Lines in R3
   3. Lines: Cartesian to parametric form
   4. Lines: Parametric and Cartesian forms given two points
   5. Lines: Convert Parametric to Cartesian
   6. Cartesian to parametric form of line
3. Planes and vectors
   1. The span of a vector
   2. Equation of plane: Parametric vector form
   3. Planes: Cartesian to parametric form
   4. Equation of plane from 3 points
4. Dot and cross product
   1. What is the dot product?
   2. Orthogonal vectors
   3. Scalar Projection of vectors
   4. Distance between a point and a line in R3
   5. Cross product of two vectors
   6. Properties of the cross product
   7. What does the cross product measure?
   8. Scalar triple product
   9. What does the scalar triple product measure?
   10. Equation of plane in R3
   11. Distance between a point and a plane in R3
5. Bibliography