Let a unit vector O P make angles α, β, γ with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where β (0, (π)/2). If OP is perpendicular to the plane through points (1,2,3),(2,3,4) and (1,5,7), then which one of the following is true?

(A) α ((π)/2, π) and γ ((π)/2, π)

(B) α (0, (π)/2) and γ ((π)/2, π)

(C) α ((π)/2, π) and γ (0, (π)/2)

(D) α (0, (π)/2) and γ (0, (π)/2)

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Morning shift · Q5833

JEE Main 202330 Jan, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let a unit vector

\widehat{O P}

make angles

\alpha, \beta, \gamma

with the positive directions of the co-ordinate axes

\mathrm{OX}

\mathrm{OY}, \mathrm{OZ}

respectively, where

\beta \in\left(0, \frac{\pi}{2}\right)

. If

\widehat{\mathrm{OP}}

is perpendicular to the plane through points

(1,2,3),(2,3,4)

and

(1,5,7)

, then which one of the following is true?