Implicitly Defined Surface

Geometry Level 4

In a 3D coordinate system, vector \(\vec{P}\) is drawn from the origin to the point \((-5,3,9)\). Consider a closed surface defined by the set of points \(\vec{Q}\) such that:

\[\large{\vec{Q} \cdot (\vec{P} - \vec{Q}) = 0}\]

Determine the volume enclosed by the surface (to 3 decimal places).

Note: The symbol "\(\large{\cdot}\)" denotes the dot product operation


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