My Math Forum Distance between two straight lines

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May 8th, 2017, 05:50 PM   #1
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Distance between two straight lines

Hello
Anyone help me to find the distance between the straight lines attached.
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 May 9th, 2017, 02:16 AM #2 Senior Member     Joined: Feb 2010 Posts: 679 Thanks: 127 A
May 9th, 2017, 02:53 AM   #3
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Quote:
 Originally Posted by mrtwhs A
Yeah. I got the process for it.

Thank you

 May 9th, 2017, 03:35 AM #4 Global Moderator   Joined: Dec 2006 Posts: 19,054 Thanks: 1618 (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, 05:33 PM   #5
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Quote:
 Originally Posted by skipjack (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.
This question can have multiple answers. So can we consider the answers as $\displaystyle \frac{\sqrt{21}}{3}$ and $\displaystyle \frac{21}{9}$?

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