If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then the direction cosines of a line perpendicular to both the lines are

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$(\frac{1}{3}, - \frac{1}{3}, \frac{2}{3})$

$(- \frac{2}{3}, - \frac{1}{3}, \frac{2}{3})$

$(\frac{2}{3}, - \frac{1}{3}, \frac{2}{3})$

$(\frac{2}{\sqrt{14}}, - \frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}})$

answer is B.

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Detailed Solution

$|\begin{matrix} \bar{i} & \bar{j} & \bar{k} \\ 1 & - 2 & - 2 \\ 0 & 2 & 1 \end{matrix}| = 2 \bar{i} - \bar{j} + 2 \bar{k} ∴ d c' s (\frac{2}{3}, \frac{- 1}{3}, \frac{2}{3})$

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