The foot of perpendicular from the origin to a plane which meets the co-ordinate axes at the points is . If the volume of the tetrahedron is , then which of the following points is NOT on ?

Explanation: 1. Equation of the Plane and Intercepts Equation of plane is The points of intersection with the axes are: 2. Volume of the Tetrahedron We have the volume of the tetrahedron: 3. Solving for 'a' and Final Equation satisfies the above equation. Substituting back into the plane equation: The point is .

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The foot of perpendicular from the origin $O$ to a plane $P$ which meets the co-ordinate axes at the points $A, B, C$ is $(2, a, 4), a \in \mathbb{N}$ . If the volume of the tetrahedron $OABC$ is $144 \text{ unit}^3$ , then which of the following points is NOT on $P$ ?

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