The angle between two lines having direction ratios $1, - 2, - 2$ and $2, - 2, 1$ is

\frac{π}{4}

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{cos}^{- 1} \frac{3}{7}

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{cos}^{- 1} (\frac{4}{9})

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\frac{π}{6}

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Solution

The correct option is C ${cos}^{- 1} (\frac{4}{9})$
$cos θ = \frac{l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2}}{\sqrt{l_{1}^{2} + m_{1}^{2} + n_{1}^{2}} \sqrt{l_{2}^{2} + m_{2}^{2} + n_{2}^{2}}}$
Given $(l_{1}, m_{1}, n_{1}) = (1, - 2, - 2)$
$(l_{2}, m_{2}, n_{2}) = (2, - 2, 1)$
$cos θ = \frac{1 (2) + 2 (2) + 1 (- 2)}{\sqrt{4 + 4 + 1} \sqrt{4 + 4 + 1}}$
$= \frac{4}{3 \times 3}$
$cos θ = \frac{4}{9}$
$θ = {cos}^{- 1} (\frac{4}{9})$

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