Mathematics - Vector Question with Solution | TestHub

Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k},\vec{b}=3\hat{i}-3\hat{j}+3\hat{k}$, $\overrightarrow{\mathrm{c}}=2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{d}}$ be a vector such that $\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{d}}=\overrightarrow{\mathrm{c}}\times \overrightarrow{\mathrm{d}}$ and $\overrightarrow{\mathrm{a}}\cdot \overrightarrow{\mathrm{d}}=4$. Then $|(\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{d}}){|}^2$ is equal to ______ .