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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.
Thanks in advance!
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May 9th, 2017, 02:16 AM   #2
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A
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May 9th, 2017, 02:53 AM   #3
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Originally Posted by mrtwhs View Post
A
Yeah. I got the process for it.

Thank you
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May 9th, 2017, 03:35 AM   #4
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(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.
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May 21st, 2017, 05:33 PM   #5
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Quote:
Originally Posted by skipjack View Post
(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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