Find the shortest distance between the lines- r- - -2- -k- - - - -k- r- -2- - -k- - 2- - -2k-

a⃗ ⃗_⃗ ⃗1⃗ =î +2ĵ +k̂ ;b⃗ ⃗_⃗ ⃗1⃗ =î ĵ +k̂ a⃗ ⃗_⃗ ⃗2⃗ =2î ĵ k̂ ;b⃗ ⃗_⃗ ⃗2⃗ =2î +ĵ +2k̂ ( a⃗ ⃗_⃗ ⃗2⃗ a⃗ ⃗_⃗ ⃗1⃗ #160; ) =î 3ĵ 2k̂ b⃗ ...

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Shortest Distance between Two Skew Lines

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Question

Find the shortest distance between the lines.
$\to r =^i + 2^j +^k + λ (^i -^j +^k)$
$\to r = 2^i -^j -^k + μ (2^i +^j + 2^k)$

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Solution

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Similar questions

\to r = (^i + 2^j +^k) + λ (^i -^j +^k)

\to r = 2^i -^j -^k + μ (2^i +^j + 2^k)

\to r =^i +^j + λ (2^i -^j +^k)

\to r = 2^i +^j -^k + μ (3^i - 5^j + 2^k)

\to r = (^i + 2^j + 3^k) + λ (^i -^j +^k)

\to r = (2^i -^j -^k) + μ (-^i +^j -^k)

l_{1}

l_{2}

\to r =^i +^j + μ (2^i -^j +^k)

\to r = 2^i +^i -^k + μ (3^i - 5^j + 2^k)

\to r =^i +^j -^k + λ (^i + 2^j + 3^k)

\to r = 3^i -^j +^k + μ (^i +^j +^k)

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