Finding the Distance Between Two Skew Lines

A note to our fellow Prep Workshop colleagues:
The audience for this web assignment will be calculus students in our community college classes. The instructional problem we are trying to solve is that students have difficulty visualizing skew lines. Instructors also have difficulty producing good images of these lines and their planes on the chalkboard. We're hoping this project helps both groups. This web assignment will be used in face-to-face classes or as part of an online class. In the future, we will provide interactive, automated feedback to the users. For the "Explain" boxes, we will insert "Submit" buttons and parse the answers.

This was our first experience with Maple and Dreamweaver, so we have learned a lot. We work at Chesapeake College, a community college serving five counties on the Eastern Shore of Maryland.

General instructions about this problem set:
You may already know how to find the distance between a point and a plane, and the distance between a point and a line. In this assignment, you will study the distance between two skew lines. You will need pencil and paper to do the math. Enter your answers to see if they are correct!!

The Problem

Consider the line in space represented by the following equation and illustration.

Now, consider a second line in space represented by the following equation and illustration.

Illustrations of line 1 and line 2:

C. Show that these two lines lie in parallel planes.
Here are images of the lines:
	Enter the equation in the following form: ax + by + cz = d
	X+ Y+ Z=

Find the distance between the two planes. This is the distance between the origin.

Enter your answer here:     squr