8 The line segment \(A B\) is a diameter of a sphere, \(S\). The point \(C\) is any point on the surface of \(S\).
- Explain why \(\overrightarrow { \mathrm { AC } } \cdot \overrightarrow { \mathrm { BC } } = 0\) for all possible positions of \(C\).
You are now given that \(A\) is the point ( \(11,12 , - 14\) ) and \(B\) is the point ( \(9,13,6\) ).
- Given that the coordinates of \(C\) have the form ( \(2 p , p , 1\) ), where \(p\) is a constant, determine the coordinates of the possible positions of \(C\).
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