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While playing around with dot product in 2D, I realized it's scalar projection behavior is directly related to power of point in Euclidean Geometry.

I am wondering if there is any notion similar to power of point in higher dimension or other branches of geometry.

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The power of a point with respect to a circle in a plane is easily generalized to spheres in 3D space, and similarly for higher dimensions. The notions of distance and radius still apply.

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