Let $\pi_1$ be the plane determined by the vectors $\bar{i}+\bar{j}, \bar{i}+\bar{k}$ and $\pi_2$ be the plane determined by the vectors $\bar{j}-\bar{k}, \bar{k}-\bar{i}$. Let $\bar{a}$ be a non-zero vector parallel to the line of intersection of the planes $\pi_1$ and $\pi_2$. If $\bar{b}=\bar{i}+\bar{j}-\bar{k}$ then the angle between the vectors $\bar{a}$ and $\bar{b}$ is

• Correct answer
  A

  $\operatorname{Cos}^{-1}\left(\sqrt{\frac{2}{3}}\right)$
• B

  $\frac{\pi}{2}$
• C

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

  $\operatorname{Cos}^{-1}\left(\frac{\sqrt{2}}{3}\right)$

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