Vector Algebra

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