Let a and b be two vectors such that | a + b |^2=| a |^2+2| b |^2, a · b =3 and | a × b |^2=75. Then | a |^2 is equal to \ \ \ \.

Let $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ be two vectors such that $\displaystyle |\vec{a}+\vec{b}|^2=|\vec{a}|^2+2|\vec{b}|^2, \vec{a} \cdot \vec{b}=3$ and $\displaystyle |\vec{a} \times \vec{b}|^2=75$. Then $\displaystyle |\vec{a}|^2$ is equal to \_\_\_\_.