08Coincident and Parallel Lines and Intersection of Lines

08Coincident and Parallel Lines and Intersection of Lines -...

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C OINCIDENT AND P ARALLEL L INES AND I NTERSECTION OF L INES Two lines in space are either parallel , intersecting , or skew . θ Skew lines are lines that are neither parallel nor intersecting. If the lines are parallel, the angle between them is 0º. If the lines are intersecting, the angle between them is . If the lines are skew, there is still an angle that one line makes with the other and if we translate one line to intersect the other, the angle between the original lines is defined as the angle between the intersecting lines. Ex . Line 1 has equation - + - = 4 2 2 1 1 1 s z y x . Line 2 has equation - - + = 2 1 1 3 0 1 t z y x . Show that lines 1 and 2 are parallel.
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Unformatted text preview: Ex . Line 1 has equation -+ -= 4 2 2 1 1 1 s z y x , line 2 has equation --+ = 2 1 1 3 1 t z y x , and line 3 has equation -+ -= 3 1 2 4 1 1 u z y x . a) Show that lines 2 and 3 intersect and find the angle between them. b) Show that lines 1 and 3 are skew. Assign: MSL p.416 Exercise 17G #1....
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This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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08Coincident and Parallel Lines and Intersection of Lines -...

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