Let for a triangle ABC, AB = -2i + j + 3k, CB = αi + βj + γk and… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 13 April, Shift 2Cross Product

Let for a triangle ABC, $\overrightarrow{AB} = -2\hat{i} + \hat{j} + 3\hat{k}$ , $\overrightarrow{CB} = \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$ and $\overrightarrow{CA} = 4\hat{i} + 3\hat{j} + \delta\hat{k}$ . If $\delta > 0$ and the area of the triangle ABC is $5\sqrt{6}$ , then $\overrightarrow{CB} \cdot \overrightarrow{CA}$ is equal to:

A
$108$
B
$60$
C
$54$
D
$120$

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