The acute angle between the diagonals OG and AD of the cuboid (shown in the figure) is

cos-1\((\frac{1}{3})\) cos-1\((-\frac{1}{3})\) cos-1\((\frac{7}{9})\) cos-1\((\frac{1}{9})\)

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

$\vec{OG}=(2\hat i + 2 \hat j + \hat k)$ $\vec{AD}=\vec{OD}-\vec{OA}=(2\hat i+\hat k)-(2\hat j)$ $= 2\hat i - 2 \hat j + \hat k$ Let θ be the angle between $\vec{OG} \And \vec{AD}$ $\cos θ =\frac{4-4+1}{3×3}⇒\cos θ =\frac{1}{9}$ $∴θ =\cos^{-1}(\frac{1}{9})$