Find the shortest distance between lines r-6 -2 -2 k-2 -2 k-and r-4 -k-3 -2 -2 k-

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Conditions for a system of linear equations to have a unique solution

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Question

Find the shortest distance between lines

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\to r = 6^i + 2^j + 2^k + λ (^i - 2^j + 2^k)

\to r = - 4^i -^k + μ (3^i - 2^j - 2^k)

Find the shortest distance between the lines
$r = 6^i + 2^j + 2^k + λ (^i - 2^j + 2^k) a n d r = - 4^i -^k + μ (3^i - 2^j + 2^k)$

\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 + 2^j +^k + λ (^i -^j +^k)

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

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

\to r = (4^i + 5^j + 6^k) + μ (2^i + 3^j +^k)

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