## Vectors

[11 May 2008]

Many readers of Interactive Mathematics have asked me to write a chapter on vectors.

Well, your wish is my command and here you go: Vectors.

The chapter starts with an overview of what vectors are and vector notation.

Then the discussion proceeds through one-dimensional vectors, through 2-D vectors (containing a Flash-based aircraft landing activity) and leading to the juicy 3-D vectors stuff like cross product.

There is a brief section on vector calculus, including a discussion on time rate of change of the position vector in elliptical motion, which is used in building Flash-based games.

I added a section at the end on the interesting topic of vector art. Digital artists produce vector graphics in image editing programs like Photoshop or the open source Inkscape. The advantages are many, ranging from scalability and small file sizes.

This guitar is an example of vector art.

I’ll be adding more discussion, examples and exercises into the chapter when I get the chance − hopefully soon!

Let me know what you think about the Vectors chapter, including your suggestions for things you’d like to see added in there.

### 2 Comments on “Vectors”

1. Li-sa says:

Small mistake made in “Vector Calculus”:
In the second example involving 3D vectors, at the specific time t = 4 s, the rate of change of the vector will be
not 5 i + 3 j + 8 k m/s^3
but 5 i + 2 j + 8 k m/s^3 as the y-component is a constant 2.

How is the alternative form of the dot product derived?

How do the dot and cross products work, like the dot product in calculating work done (Work=F s cos A)? Could you please show us why these formulas are so odd?

2. Murray says:

Hi Li-sa

Thanks for the typo correction – fixed.

I have added a proof of the alternative dot product and I will generalise it more later.

I’ll keep your dot and cross product requests in mind when I add further examples and explanations – soon!

XHTML: You can use these tags: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>