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Vector Algebra question

2023 · 30 Jan · Shift 1 · Q31

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2023 · 30 Jan · Shift 1 · Q31

Vector Algebra question

2023 · 30 Jan · Shift 1 · Q31

JEE MainMathematicsVector AlgebraMCQ+4 / −1

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?

A
$\alpha \in\left(\frac{\pi}{2}, \pi\right)$ and $\gamma \in\left(\frac{\pi}{2}, \pi\right)$
B
$\alpha \in\left(0, \frac{\pi}{2}\right)$ and $\gamma \in\left(\frac{\pi}{2}, \pi\right)$
C
$\alpha \in\left(\frac{\pi}{2}, \pi\right)$ and $\gamma \in\left(0, \frac{\pi}{2}\right)$
D
$\alpha \in\left(0, \frac{\pi}{2}\right)$ and $\gamma \in\left(0, \frac{\pi}{2}\right)$

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