Let \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}\) and \(\vec{c}=-\hat{i}+4 \hat{j}+3 \h…

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}\) and \(\vec{c}=-\hat{i}+4 \hat{j}+3 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{b}\) and \(\vec{c}\) and \(\vec{a} \cdot \vec{d}=18\). Then \(|\vec{a} \times \vec{d}|^2\) is equal to:

[JEE Main 2023, 6 Apr (Shift 1)]