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Shortest distance between r = (4i - j) + l(i + 2j - 3k) and r = (i - j + 2k) + m(i + 4j - 5k)

The same question, asked 2 times: 21 Apr 2025 S1*, 19 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    21 Apr 2025 S1

    104
    The shortest distance between the lines r‾=(4i^−j^)+λ(i^+2j^−3k^)\overline{r}= (4\widehat{i}-\widehat{j}) +\lambda(\widehat{i}+ 2\widehat{j}- 3\widehat{k}) and r‾=(i^−j^+2k^)+μ(2i^+4j^−5k^)\overline{r}= (\widehat{i}-\widehat{j}+ 2\widehat{k}) +\mu(2\widehat{i}+ 4\widehat{j}- 5\widehat{k}) is

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  2. Question 2

    19 Apr 2026 S2

    93
    The shortest distance between the lines r⃗=(4i^−j^)+λ(i^+2j^−3k^)\vec{r} = (4\hat{i} - \hat{j}) + \lambda(\hat{i} + 2\hat{j} - 3\hat{k}) and r⃗=(i^−j^+2k^)+μ(i^+4j^−5k^)\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(\hat{i} + 4\hat{j} - 5\hat{k}) is...

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