Step-by-step Solution:

Fundamentally this question is wrong because sum of two vectors can not be equal to scalar. But if we have solve this question. \[ |2 \vec{a} + \vec{b}|^2 = 9 \] \[ 4|\vec{a}|^2 + |\vec{b}|^2 + 4 \vec{a} \cdot \vec{b} = 9 \] \[ |\vec{a}| |\vec{b}| \cos \theta = 1 \] Since \( \cos \theta = 1 \), this implies: \[ \theta = 0 \] Thus, the vectors \( \vec{a} \) and \( \vec{b} \) are parallel.