Vector Algebra

Let \(\vec{a}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\vec{c}=2 \hat{i}-3 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\vec{a}=\vec{b} \times \vec{c}\) and \(|\vec{b}|^{2}=50\), then \(|72-| \vec{b}+\left.\vec{c}\right|^{2} \mid\) is equal to __________.