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The shortest distance between the lines $r = (4 i - j) + λ (i + 2 j - 3 k)$ and $r = (i - j + 2 k) + μ (2 i + 4 j - 5 k)$ is

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detailed solution

Correct option is C

d=[(4i−j)−(i−j+2k)]⋅(i+2j−3k)×(2i+4j−5k)|(i+2j−3k)×(2i+4j−5k)|=(3i−2k)⋅(2i−j)|2i−j|=65.

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The shortest distance between the lines r=(4i−j)+λ(i+2j−3k) and r=(i−j+2k)+μ(2i+4j−5k) is

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The shortest distance between the lines $r = (4 i - j) + λ (i + 2 j - 3 k)$ and $r = (i - j + 2 k) + μ (2 i + 4 j - 5 k)$ is