A plane $\pi_1$ contains the vectors $\bar{i}+\bar{j}$ and $\bar{i}+2 \bar{j}$. Another plane $\pi_2$ contains the vectors $2 \bar{i}-\bar{j}$ and $3 \bar{i}+2 \bar{k} \cdot \bar{a}$ is a vector parallel to the line of intersection of $\pi_1$ and $\pi_2$. If the angle $\theta$ between $\bar{a}$ and $\bar{i}-2 \bar{j}+2 \bar{k}$ is acute, then $\theta=$

• A

  $\frac{\pi}{2}$
• B

  $\frac{\pi}{4}$
• Correct answer
  C

  $\operatorname{Cos}^{-1}\left(\frac{4}{3 \sqrt{5}}\right)$
• D

  $\operatorname{Cos}^{-1}\left(\frac{2}{\sqrt{5}}\right)$

Hence, the correct answer is option: 'C'.