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Question

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

60
54
120
108

Solution

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