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#### • two skew lines

Question:i am doing a project and i was absent for the definition of skew lines. now we have to find examples of skew lines in real life. for example and over pass on a highway? please help me find image links or sites? Oh yeah and they have to demonstrate function

Question:As a follow-on to http://answers.yahoo.com/question/index?qid=20080404190545AAwI6UO and referring to this diagram: http://nrich.maths.org/askedNRICH/edited/2360.html (but using my notation, not his) I want to talk about the general eqn for line PQ, NOT just shortest distance itself. Two questions: 1) Critique my working and suggest any improvements. 2) We end up with three eqns in two parametric variables (s,t). How can we be sure that this overdetermined system has any solution in s,t? Given any two skew (non-intersecting) lines: Line LP : x = a + sb Line LQ : x = c + td >Hint: the line joining P and Q is perpendicular to both lines PQ must be parallel to (a b), so form the unit vector in that direction: n = (a b) / ||a b|| Now take any (non-shortest) vector which is known to go between lines LP and LQ, such as (c-a), and project it onto n: a + sb ||(c -a) . n|| n = c + td (a-c) ||(a-c) . n|| n = (td -sb) => Three eqns in two variables s,t I think the missing third variable is r, an arbitrary-length vector in the direction of n. => Three eqns in three variables Or something like that. Please help tie up this loose end and rewrite: (a-c) ||(a-c) . n|| n = (td -sb) scythian - thanks. It simplifies a bit if we write (a-c) =u in: e = (a-c) +Sb -Td = u +Sb -Td Can you simplify your result algebraically? It looks like a determinant, or two separate determinants to me?

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.

Question:more specifically around 15th century Europe and 12th-19th century Japan. Thanks You guys please read the fucking time period and region!

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.

Question:I'm trying to build a model house for Geometry, and need some real life examples for these geometric shapes you may see in your house or on the outside of the house. Thanks!!!! Transversal line Parallel Lines Kite Alternate Interior Angles Same-Side Interior Angles Corresponding Angles Bonus Shapes Circle, Dodecagon

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...