Let $\lambda \in Z, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}$. Let $\vec{c}$ be a vector such that $(\vec{a}+\vec{b}+\vec{c}) \times \vec{c}=\overrightarrow{0}, \vec{a} \vec{c}=-17$, $\bar{b} \cdot \bar{c}=-20$. Then $|\vec{c} \times(\lambda \hat{i}+\hat{j}+\hat{k})|^2$ is equal to