The centroid of a triangle \( A B C \) is at the point \( (1,1,1) \). If the coordinates of \( A...

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The centroid of a triangle \( A B C \) is at the point \( (1,1,1) \). If the coordinates of \( A \) and \( B \) are \( (3,-5,7) \) and \( (-1,7,-6) \) respectively, find the coordinates of the point \( C \).
(a) \( (1,-1,3) \)
(b) \( (1,1,2) \)
(c) \( (-1,-1,-3) \)
(d) \( (2,-1,3) \)
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