Let \( \vec{c} \) be the projection vector of \( \vec{b}=\lambda \hat{i}+4\hat{k},\, \lambda>0 \), on the vector \( \vec{a}=\hat{i}+2\hat{j}+2\hat{k} \). If \( |\vec{a}+\vec{c}|=7 \), then the area of the parallelogram formed by the vectors \( \vec{b} \) and \( \vec{c} \) is ______.
