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MCQMediumJEE Main 2023 · 30 January, Shift 1Equation of Plane

Mathematics Question from JEE Main 2023 · 30 January, Shift 1

Let a unit vector OP→\overrightarrow{OP} make angles α,β,γ\alpha, \beta, \gamma with the positive directions of the coordinate axes OX,OY,OZOX, OY, OZ respectively, where β∈(0,π2)\beta \in \left( 0, \frac{\pi}{2} \right), and OP→\overrightarrow{OP} is perpendicular to the plane through points (1,2,3)(1, 2, 3), (2,3,4)(2, 3, 4), and (1,5,7)(1, 5, 7). Then which one of the following is true?

  • A

    α∈(π2,π)\alpha \in \left( \frac{\pi}{2}, \pi \right) and γ∈(π2,π)\gamma \in \left( \frac{\pi}{2}, \pi \right)

  • B

    α∈(0,π2)\alpha \in \left( 0, \frac{\pi}{2} \right) and γ∈(0,π2)\gamma \in \left( 0, \frac{\pi}{2} \right)

  • C

    α∈(π2,π)\alpha \in \left( \frac{\pi}{2}, \pi \right) and γ∈(0,π2)\gamma \in \left( 0, \frac{\pi}{2} \right)

  • D

    α∈(0,π2)\alpha \in \left( 0, \frac{\pi}{2} \right) and γ∈(π2,π)\gamma \in \left( \frac{\pi}{2}, \pi \right)

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