Let a =6 i +9 j +12 k, b =α i +11 j -2 k and c be vectors such that a × c = a × b. If a · c =-12, c ·( i -2 j + k )=5, then c ·( i + j + k ) is equal…

Let $\displaystyle \vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}$ and $\displaystyle \vec{c}$ be vectors such that $\displaystyle \vec{a} \times \vec{c}=\vec{a} \times \vec{b}$. If $\displaystyle \vec{a} \cdot \vec{c}=-12, \vec{c} \cdot(\hat{i}-2 \hat{j}+\hat{k})=5$, then $\displaystyle \vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})$ is equal to $\displaystyle \_\_\_\_$.