Distance_Between_Two_Non_Parallel_Lines - Distance Between...

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Unformatted text preview: Distance Between Two Non Parallel Lines Line 1 : x = 2 + u, y = 1 + 6u, z = 2u Line 2 : 2 + 4v, y = 5 + 13v, z = -1 + 6v As in all “shortest d stance” problems, the shortest l ne connecting and is perpendicular to both. Start by separating P and Q from the directional vectors that they lie on. ne u ne v Where points P and Q are and respectively and vectors and are and respectively. Vector is easy to calculate. Notice it is simply the vector sum of red vector (when pointing downwards) plus the two dark green vectors. The two dark green vectors are parallel to and which means they are perpendicular to the red vector. So how do we get rid of them? Projecting onto a vector perpendicular to the dark green vectors will leave us with simply the red vector. What is perpendicular to and ? Their cross product: . Take the magnitude and we have the solution. d d pro u v d ...
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This note was uploaded on 12/01/2010 for the course MATH 133 taught by Professor Klemes during the Fall '08 term at McGill.

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