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From any point perpendiculars PM and PN are drawn to ZX and XY planes. If O is the origin, find the…
From any point $P(2, 1, 2)$ perpendiculars PM and PN are drawn to ZX and XY planes.
(a)
If O is the origin, find the equation of the plane OMN.
(b)
Find $\theta$, if $\theta$ is the angle made by OP with the plane OMN.
(c)
If $\alpha, \beta$ and $\gamma$ are the angles made by OP with the co-ordinate planes, prove that $\csc^2 \theta = \csc^2 \alpha + \csc^2 \beta + \csc^2 \gamma$.
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From ISC 2025 Practice Mathematics, question 114.