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 N. If the volume of the tetrahedron OABC is 144 unit ³, then which of the following points is NOT on P ?

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 31 Jan, Evening shift · Q2455

JEE Main 202331 Jan, Evening shiftMathematicsHardThree Dimensional Geometry249× since 2002

The foot of perpendicular from the origin

\mathrm{O}

to a plane

\mathrm{P}

which meets the co-ordinate axes at the points

\mathrm{A}, \mathrm{B}, \mathrm{C}

(2, \mathrm{a}, 4), \mathrm{a} \in \mathrm{N}

. If the volume of the tetrahedron

\mathrm{OABC}

is 144 unit

^{3}

, then which of the following points is NOT on P ?