- #1

HF08

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**R**[tex]^{3}[/tex] that are not parallel but do not intersect.

My Thoughts:

I have never seen this type of question before and the material in my text is unfortunately lacking. However, I was able to piece these thoughts together.

The cross product of three vectors should not equal zero. (Otherwise they are orthogonal, and hence intersect).

None of the vectors should be multiples of the other vectors.

So my question is, I can draw to lines in R^3 space that don't intersect. I suppose I

could find two lines by taking z2 -z1 where z = f(x,y) but this feels sloppy. Can someone

help me construct something more formally with logic and method?

Thank You,

HFO8