Let three vectors $\vec{a}=\alpha \hat{\imath}+4 \hat{\jmath}+2 \hat{k}, \vec{b}=5 \hat{\imath}+3 \hat{\jmath}+4 \hat{k}, \vec{c}=x \hat{\imath}+y \hat{\jmath}+z \hat{k}$ from a triangle such that $\vec{c}=\vec{a}-\vec{b}$ and the area of the triangle is 5√6. if α is a positive real number, then $|\vec{c}|^2$ is: