Let a =2 i +7 j - k, b =3 i +5 k and c = i - j +2 k. Let d be a vector which is perpendicular to both a and b, and c · d =12. Then (- i + j - k ) ·(…

Let $\displaystyle \vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}$ and $\displaystyle \vec{c}=\hat{i}-\hat{j}+2 \hat{k}$. Let $\displaystyle \vec{d}$ be a vector which is perpendicular to both $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$, and $\displaystyle \vec{c} \cdot \vec{d}=12$. Then $\displaystyle (-\hat{i}+\hat{j}-\hat{k}) \cdot(\vec{c} \times \vec{d})$ is equal to