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If r = (6i+2j+2k) + t(i-2j+2k) & r = (-4i-k) + s(3i-2j-2k) represents equations of two straight lines, then the least distance between them is?

If r = (6i+2j+2k) + t(i-2j+2k) & r = (-4i-k) + s(3i-2j-2k) represents equations of two straight lines, then the least distance between them is?

Grade:12th Pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
The two lines given are r = (6i + 2j + 2k) + t(i – 2j + 2k) and r = (- 4i – k) + s(3i – 2j – 2k).
For two lines x = a + tb and y = c + sd, the shortest distance between them are 
d = | bxd/|bxd| . (c – a) | = |(8i + 8j + 4k).(-10i – 2i – 3k)/12| = |(- 80 – 16 – 12)/12| = 108/12 = 9.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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