The velocity of the centre of mass of a rigid rod with respect to an observer $O$ is $\vec v_{cm} = (2\hat i + 3\hat j) \text{ m/s}$. The rod has an angular velocity about its centre of mass given by $\vec \omega = (3\hat j + 4\hat k) \text{ rad/s}$. Let $A$ be a point on the rod with position vector $\vec r = 2(\hat i + \hat k) \text{ m}$ with respect to the centre of mass. The velocity of the point $A$ with respect to $O$ is:

• A
  $6\hat i + 11\hat j + 6\hat k$
• B
  $8\hat i + 11\hat j - 6\hat k$
• C
  $6\hat i - 11\hat j + 12\hat k$
• D
  $8\hat i + 11\hat j - 8\hat k$