IF a and b are on different planes A and B,

A//B

must a//b?

Draw a picture. Hint, you may as well suppose that A and B are in fact the same plane.

I infer that they may not be parallel.

Is it correct?

Can you draw two non-parallel lines in parallel planes? Of course you can. (Note, in 3-d the definition of parallel is that the minimal distance from a point on one line to the other line is constant; it is not that the lines do not intersect.)

IF a and b are on different planes A and B' date='

A//B

must a//b?[/quote']

 

 

 

No they are not always parallel. As there is no such condition that if planes are parallel then the points/ lines on them are parallel.

They will either be parallel or skew (http://mathworld.wolfram.com/SkewLines.html).

 

Edit: Url fixed, thanks swansont.

They will either be parallel or skew (http://mathworld.wolfram.com/SkewLines.html)[/url'].

 

 

 

http://mathworld.wolfram.com/SkewLines.html

 

(Markup tag topology error. You have a parenthesis in your url.)

ok thanks guys.