Let $\vec{a}=2 \hat{\imath}+5 \hat{\jmath}-\hat{k}, \vec{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be three vectors such that $(\vec{c}+\hat{\imath}) \times(\vec{a}+\vec{b}+\hat{\imath})=\vec{a} \times(\vec{c}+\hat{\imath})$. $\vec{a} \cdot \vec{c}=-29$, then $\overrightarrow{\mathrm{c}} \cdot(-2 \hat{\imath}+\hat{\jmath}+\hat{\mathrm{k}})$ is equal to :