This problem involves vector geometry and properties of triangles. Given the information, we need to express the angles and areas in terms of the given vectors or lengths. However, without a specific

This problem involves vector geometry and properties of triangles. Given the information, we need to express the angles and areas in terms of the given vectors or lengths. However, without a specific angle for $\angle AOB$ or specific lengths for $a$ and $b$, it is not possible to find numerical values for the angles in part (a) or the areas in part (b). The question asks for "the size of angle", implying a numerical value. This suggests that either there is missing information in the problem statement (e.g., $\angle AOB = 90^\circ$ or $60^\circ$, or specific values for $a$ and $b$), or the question expects the angles to be expressed in terms of $\angle AOB$. Given the typical context of such problems