# Skew lines and line projection

Please help me with this.A line is perpedicular to one of the two skew lines. That means is also perpedicular to the other one?

No, it doesn't imply that. But it can happen.

You can easily see it with 3 pencils/pens:

Put three pencils on a table like this: |_|

If you make the pencil from the right normal to the table, then the far left and far right pencils are skew and both perpendicular to the pencil in the middle. If you now rotate the pencil from the right a little bit in a different plane from the first rotation, you get that the middle pencil is perpendicular to one of the skew pencils but not perpendicular to the other.

• By the way, this is not a mathematical argument, it's just an appeal to a physical experiment/visualization. I think it helps. Mar 23, 2014 at 17:18
• P.S. I just noticed I could've described it better using a cube's vertices ABCDEFGH and a few other points on its edges. Mar 23, 2014 at 17:55
• I'm trying my best to be specific, but is really difficult for me because I am not fluent in English. Mar 23, 2014 at 19:02
• this line links the two skew lines..I guess that was really important to tell you firstly Mar 23, 2014 at 19:04
• I think that my answer satisfy that. I will upload pictures of what I thought. But I don't know if they are going to be good... Mar 24, 2014 at 2:50