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Question

# The points $P(a, b, c)$ and $Q(2,3,5)$ are symmetric in the sense given. Find $a, b, c$. About the plane $z=4$.

Solution

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The distance from point $Q(2,3,5)$ to the plane $z=4$ is equal to the distance from point $P(a,b,c)$ to the plane $z=4$.

The value of that distance is $1$.

Furthermore, the segment joining $P$ and $Q$ is perpendicular to the plane $z=4$.

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