Determine the point on \( z \)-axis which is equidistant from the points \( (1,5,7) \) and \( (5...

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Determine the point on \( z \)-axis which is equidistant from the points \( (1,5,7) \) and \( (5,1,-4) \).
(a) \( \left(0,0, \frac{1}{2}\right) \)
(b) \( \left(0,0, \frac{3}{2}\right) \)
(c) \( \left(0, \frac{3}{2}, 0\right) \)
(d) \( \left(0,0, \frac{5}{2}\right) \)
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