jee-main 2023 Q76

jee-main · India · session2_13apr_shift2 Vectors 3D & Lines Vector Algebra and Triple Product Computation
Let for a triangle $ABC$ $$\begin{aligned} & \overrightarrow { AB } = - 2 \hat { i } + \hat { j } + 3 \hat { k } \\ & \overrightarrow { CB } = \alpha \hat { i } + \beta \hat { j } + \gamma \hat { k } \\ & \overrightarrow { CA } = 4 \hat { i } + 3 \hat { j } + \delta \hat { k } \end{aligned}$$ If $\delta > 0$ and the area of the triangle $ABC$ is $5 \sqrt { 6 }$ then $\overrightarrow { CB } \cdot \overrightarrow { CA }$ is equal to
(1) 60
(2) 54
(3) 108
(4) 120
Let for a triangle $ABC$
$$\begin{aligned}
& \overrightarrow { AB } = - 2 \hat { i } + \hat { j } + 3 \hat { k } \\
& \overrightarrow { CB } = \alpha \hat { i } + \beta \hat { j } + \gamma \hat { k } \\
& \overrightarrow { CA } = 4 \hat { i } + 3 \hat { j } + \delta \hat { k }
\end{aligned}$$
If $\delta > 0$ and the area of the triangle $ABC$ is $5 \sqrt { 6 }$ then $\overrightarrow { CB } \cdot \overrightarrow { CA }$ is equal to\\
(1) 60\\
(2) 54\\
(3) 108\\
(4) 120