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