# Application of the cross product: max height of z?

1. Feb 23, 2012

### brinethery

1. The problem statement, all variables and given/known data

http://www.scribd.com/doc/82645310

In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB.

2. Relevant equations

ABxCD

3. The attempt at a solution

ABxCD, and then make this a unit vector. Then dot this unit vector with vector AC.

The question asks "what is the maximum height z can be...". The distance from the center to the radius of the two conduits when they're touching is going to be 1.5ft (since the diameters are 1ft and 2ft respectively). This means that I'll take the two vectors I dotted and set them equal to 1.5ft. Then I'll solve for z.

Let me know if this is wrong in any way :-)

Update:

Here is what I have so far

http://www.scribd.com/doc/82663003

Last edited: Feb 24, 2012