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Could you please explain how you would use vector projection to find the closest...

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eikco | Student, Undergraduate | (Level 1) eNoter

Posted September 4, 2011 at 10:17 PM via web

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Could you please explain how you would use vector projection to find the closest approach between two skew lines.

The vectors are in 3D

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santaone | High School Teacher | (Level 3) eNoter

Posted September 12, 2011 at 12:07 AM (Answer #1)

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Let the two skew lines have equations

(x - x1)/ l1 = (y - y1)/m1 = (z - z1)/n1

 

(x - x2)/ l2 = (y - y2)/m2 = (z - z2)/n2

 

 

Then the shortest distance between the two is given by

 

D  = A/B

 

where A = (x2-x1)(m1n2-n1m2)-(y2-y1)(l1m2-l2m1)+

(z2-z1)(l1m3-l3m1)

 

 

and B = sqrt( (m1n2-m2n1)^2 + (n1l2-n2l1)^2 +(l1m2-l2m1)^2)

 

 

 

 

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