Let \(\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}\) and \(\vec{c}=2 \hat{i}-\hat{j}+4 \ha…

Let \(\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}\) and \(\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}\). If a vector \(\vec{d}\) satisfies \(\vec{d} \times \vec{b}=\vec{c} \times \vec{b}\) and \(\vec{d} \cdot \vec{a}=24\), then \(|\vec{d}|^2\) is equal to

[JEE Main 2023, 13 Apr (Shift 1)]