Let for a triangle $A B C$, $\overrightarrow{A B}=-2 \hat{i}+\hat{j}+3 \hat{k} $ $\overrightarrow{C B}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} $ $\overrightarrow{C A}=4 \hat{i}+3 \hat{j}+\delta \hat{k}$ If $\delta0$ and the area of the triangle $A B C$ is $5 \sqrt{6}$, then $\overrightarrow{C B} \cdot \overrightarrow{C A}$ is equal to [JEE Main 2023, 13 Apr (Shift 2)]

Question

Let for a triangle $A B C$, $\overrightarrow{A B}=-2 \hat{i}+\hat{j}+3 \hat{k} $ $\overrightarrow{C B}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} $ $\overrightarrow{C A}=4 \hat{i}+3 \hat{j}+\delta \hat{k}$ If $\delta>0$ and the area of the triangle $A B C$ is $5 \sqrt{6}$, then $\overrightarrow{C B} \cdot \overrightarrow{C A}$ is equal to [JEE Main 2023, 13 Apr (Shift 2)]

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Let for a triangle \(A B C\), \(\overrightarrow{A B}=-2 \hat{i}+\hat{j}+3 \hat{k} \) \(\overrightarrow{C B}=\alpha \hat{…

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