Vector Algebra

Let for a triangle \(\mathrm{ABC}\),

\(\overrightarrow{\mathrm{AB}}=-2 \hat{i}+\hat{j}+3 \hat{k}\)

\(\overrightarrow{\mathrm{CB}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}\)

\(\overrightarrow{\mathrm{CA}}=4 \hat{i}+3 \hat{j}+\delta \hat{k}\)

If \(\delta > 0\) and the area of the triangle \(\mathrm{ABC}\) is \(5 \sqrt{6}\), then \(\overrightarrow{C B} \cdot \overrightarrow{C A}\) is equal to