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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