What Skew Lines Are and Aren'tDate: 01/14/2004 at 22:53:04 From: Anita Subject: What are skew lines and how do you find them What are skew lines and how do you find them? I can not draw a figure but I hope you can understand what I mean. Date: 01/15/2004 at 13:07:51 From: Doctor Peterson Subject: Re: What are skew lines and how do you find them Hi, Anita. Skewness is not a property of a single line by itself, but a way in which two lines can be related. I'll illustrate by having you look around the room you're in, assuming it is the usual sort of rectangular room with a ceiling. Look down at the floor in the corner; you'll see this: +---------- | | | | | | Those two lines INTERSECT. That is one way in which two lines can be related. Note that they are also coplanar (since they both lie on the floor, which is (part of) a plane; any two intersecting lines lie in the same plane. Now look at the bottom edges of two opposite walls; they will look like this: -------------- -------------- These lines are PARALLEL. They are always the same distance apart; if they extended forever, they would never meet. And they, too, are coplanar. Now twist your head around and look at one of those floor edges, as well as one of the edges of the ceiling--but on an adjacent wall, not the same wall. This is harder to draw, but it will look something like this: / / / / / \ \ \ They are NOT coplanar! They do NOT intersect! They are NOT always the same distance apart! That is what SKEW lines are: a pair of noncoplanar lines, which therefore are neither parallel nor intersecting. If you chose any two lines in the world, most likely they would be skew lines. The following page has a nice picture of a pair of skew lines that you may be able to move around with your mouse to see how they look from different directions: http://mathworld.wolfram.com/SkewLines.html Have fun! And write back if you have any more questions. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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