Mathematics Question from JEE Main 2023 · 13 April, Shift 1

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