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The perpendicular distance from origin to the plane passing through the points $2 i - 2 j + k$ $3 i + 2 j - \bar{k}, 3 i - j - 2 k$ is

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$\frac{12}{\sqrt{30}}$

$\frac{25}{\sqrt{110}}$

$\frac{10}{\sqrt{60}}$

$\frac{15}{\sqrt{187}}$

answer is B.

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Detailed Solution

$\frac{| [\bar{a} \bar{b} \bar{c}] |}{| \bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a} |}$

$\Rightarrow \bar{a} = 2 \bar{i} - 2 \bar{j} + \bar{k}, \bar{b} = 3 \bar{i} + 2 \bar{j} - \bar{k}, \bar{c} = 3 \bar{i} - \bar{j} - 2 \bar{k}$

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