Mathematics - Vector Question with Solution | TestHub

Let$\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+3\hat{\mathrm{k}}$and$\overrightarrow{\mathrm{b}}=3\hat{\mathrm{i}}-\alpha \hat{\mathrm{j}}+\hat{\mathrm{k}}$. If the area of the parallelogram whose adjacent sides are represented by the vectors$\overrightarrow{a}$and$\overrightarrow{b}$is$8\sqrt{3}$square units, then$\overrightarrow{a}·\overrightarrow{b}$is equal to ___ .