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

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$\frac{10}{\sqrt{3}}$

$\frac{10}{2 \sqrt{3}}$

$\frac{10}{3 \sqrt{3}}$

$\frac{10}{3}$

answer is C.

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Detailed Solution

$a = 2 i - 2 j + 3 k ⊥ distance = |\frac{a . n - d}{|n|}| = |\frac{2 - 10 + 3 - 5}{\sqrt{1 + 25 + 1}}| = \frac{10}{\sqrt{27}}$

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