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May 8th, 2017, 06:50 PM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 206 Thanks: 2  Distance between two straight lines
Hello Anyone help me to find the distance between the straight lines attached. Thanks in advance! 
May 9th, 2017, 03:16 AM  #2 
Senior Member Joined: Feb 2010 Posts: 632 Thanks: 103 
A

May 9th, 2017, 03:53 AM  #3 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 206 Thanks: 2  
May 9th, 2017, 04:35 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,137 Thanks: 1415 
(2u, u + 1, u  1) and (2v  1, v  1, v  1) are general points on the lines. The square of the distance between them is (2u  2v + 1)² + (u  v + 2)² + (u  v)², which equals ((6u  6v + 4)² + 14)/6 and so has minimum value 14/6 = 21/9. Hence the square of the distance between the lines is 21/9. 
May 21st, 2017, 06:33 PM  #5  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 206 Thanks: 2  Quote:
 

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distance, lines, straight 
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