give me some examples of skew lines
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Answers:DEFINITION: Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. http://go.hrw.com/resources/go_mt/hm1/so/c1ch8aso.pdf http://www.icoachmath.com/SiteMap/SkewLines.html Definition of Skew Lines: Two nonparallel lines in space that do not intersect are called skew lines. Real-life examples http://www.newton.dep.anl.gov/askasci/math99/math99236.htm Skewed lines are used a lot in construction. The best example that I can think of is the Brooklyn Bridge in New York. Here's a photo of it and you'll see all the lines that are not parallel. http://www.yellowecho.com/travel/brooklyn_bridge_16.html Also, it really depends on what angle you are look at something. We all know that the sides of a road/highway are parallel, but if you are driving on the road (the road in the photo of the Brooklyn Bridge is a perfect example), do you see how lines that we know are "parallel" can look skewed at the same time? The sides of the road are parallel, but our driving on the road and from the perspective of the driver, the sides of the road don't "look" parallel (even though looking down from the sky in an airplane they would look paralel), they look skewed from within a car. Same thing with railroad tracks... if you stand on the tracks and look down they look parallel, but if from where you are standing, and you look far into the distance... it looks like the two rail track converge to a point and aren't parallel. Same thing with like if you are looking down the school hallway. The walls are in reality parallel... but from where you are standing... and look straight ahead to the other end of the school building.. it looks skewed and like the lines are not parallel. Same with if you look at a building at an angle... we all know that in reality, all the ceilings and floors of your school are parallel (or I would hope that they are!!! LOL).... But if you look at the building from and angle... All the lines of your roof, floors and ceilings... all seem to converge to one single point... So real-life examples of parallel lines.... CAN and often do look like skewed lines if you are looking at an angle. Hope this helps...
Answers:Let me try my hand in this. Let a, b, c, d be vectors in 3D space, and S, T be scalar variables, so that we have two skew lines a+Sb, c+Td. The difference, e = (a+Sb) - (c+Td), is a vector connecting the two lines, so that the shortest such vector would have the property e . b = e . d = 0. If we expand both, and solve the simultaneous equations, we end up with the following scalar quantities S, T: S = ((cd - ad) bd + (ab - cb) dd) / ((bd) - bb dd) T = ((ab - cb) bd + (cd - ad) bb) / ((bd) - bb dd) where ab, ad, cb, cd, bd, bb, dd are all vector dot products. Incidentally, the same result can be found by finding minimum S & T through partial differentiation of the vector length of e. Addendum: Well, let's see, if a - c = u, we can rewrite the equations as: S = (ub dd - ud bd) / ((bd) - bb dd) T = (ub bd - ud bb) / ((bd) - bb dd) The form does vaguely remind me of terms found in differential geometry, as for example EG - F , which is a determinant of the first fundamental form.
Answers:Gosh, you didn't even have a long question like most people do....lol. People have ADD reading just the first line.....those idiots...oh, I don't have an anwer either cause I don't remember the century you are asking about but atleast I read the question.
Answers:circle: Door knob parrallel line: on the windows... you could make it that certain type of window and include those three types of angles too...