jee-main 2023 Q77

jee-main · India · session2_10apr_shift1 Vectors 3D & Lines Section Division and Coordinate Computation

Let two vertices of a triangle $ABC$ be $(2, 4, 6)$ and $(0, -2, -5)$, and its centroid be $(2, 1, -1)$. If the image of the third vertex in the plane $x + 2y + 4z = 11$ is $(\alpha, \beta, \gamma)$, then $\alpha\beta + \beta\gamma + \gamma\alpha$ is equal to
(1) 70
(2) 76
(3) 74
(4) 72

Let two vertices of a triangle $ABC$ be $(2, 4, 6)$ and $(0, -2, -5)$, and its centroid be $(2, 1, -1)$. If the image of the third vertex in the plane $x + 2y + 4z = 11$ is $(\alpha, \beta, \gamma)$, then $\alpha\beta + \beta\gamma + \gamma\alpha$ is equal to\\
(1) 70\\
(2) 76\\
(3) 74\\
(4) 72

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