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The distance between the parallel lines $\bar{r} = 2 \bar{i} + 3 \bar{j} - \bar{k} + λ (\bar{i} - \bar{j} + 2 \bar{k})$ and $\bar{r} = - 3 \bar{i} + 4 \bar{j} + \bar{k} + μ (\bar{i} - \bar{j} + 2 \bar{k})$ is

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Correct option is A

a¯1=2i¯+3j¯−k¯, a¯2=−3i¯+4j¯+k¯, b¯=i¯−j¯+2k¯, a¯1−a¯2=5i¯−j¯−2k¯b¯×(a¯1−a¯2)=i¯j¯k¯1−125−1−2=4i¯+12j¯+4k¯|b¯×(a¯1−a¯2)|=176, |b¯|=6Distance = |b¯×(a¯1−a¯2)||b¯|=1766=2223

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

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The distance between the parallel lines $\bar{r} = 2 \bar{i} + 3 \bar{j} - \bar{k} + λ (\bar{i} - \bar{j} + 2 \bar{k})$ and $\bar{r} = - 3 \bar{i} + 4 \bar{j} + \bar{k} + μ (\bar{i} - \bar{j} + 2 \bar{k})$ is