Let \(\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}\) and \(\vec{c}=\hat{i}-\hat{j}+2 \hat{k}\). Let …

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

[JEE Main 2023, 10 Apr (Shift 2)]