Vector Algebra

Let \(\overrightarrow{\mathrm{a}}=4 \hat{i}-\hat{j}+\hat{k}, \overrightarrow{\mathrm{b}}=11 \hat{i}-\hat{j}+\hat{k}\) and \(\overrightarrow{\mathrm{c}}\) be a vector such that \((\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{c}} \times(-2 \overrightarrow{\mathrm{a}}+3 \overrightarrow{\mathrm{b}})\).
If \((2 \vec{a}+3 \vec{b}) \cdot \vec{c}=1670\), then \(|\vec{c}|^2\) is equal to: