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The distance between the line $\vec{r} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k} + λ (i - j + 4 k)$ and the plane $\vec{r} . (\hat{i} + 5 \hat{j} + \hat{k}) = 5$ is

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Correct option is B

Distance between the line r→=2i^−2j^+3k^+λ(i−j+4k) and the planer→.(i^+5j^+k^)=5 . Therefore distance of line from this plane=perpendicular distance of point (2,–2, 3)from the plane i.e. |2−10+3−51+52+1|=1033

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The distance between the line r→=2i^−2j^+3k^+λ(i−j+4k) and the plane r→.(i^+5j^+k^)=5 is

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The distance between the line $\vec{r} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k} + λ (i - j + 4 k)$ and the plane $\vec{r} . (\hat{i} + 5 \hat{j} + \hat{k}) = 5$ is