Let a =4 i - j + k, b =11 i - j + k and c be a vector such that ( a + b ) × c = c ×(-2 a +3 b ). If (2 a +3 b ) · c =1670, then | c |^2 is equal to:

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