The centroid of a collection of points (a1, b1, c1), (a2, b2, c2), (a3, b3, c3), …, (an, b...

The centroid of a collection of points (a1, b1, c1), (a2, b2, c2), (a3, b3, c3), …, (an, bn, cn,) is the point , where

This generalizes the definition of midpoint.

(a) Find the centroid of the points (−2, 5, 6), (0, 3, 0), (8, 11, 1), and (4, 2, 6).

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(b) Determine a condition on (x, y, z) so that the centroid of the three points (1, 2, 3), (−3, 3, −1), and (x, y, z) lies inside the sphere of radius 1 centered at the origin.