find the points on z axis which is equidistance from poinnt A (1,5,7) and B (5,1,-4).

Let the point on z-axis is P(0,0,z), which is equidistant from the points A(1,5,7) and B(5,1,-4)

We know the distance formula between two points is,

 ...... (1)

So, distance between the point P(0,0,z) and A (1,5,7) is,

And the distance between the point P(0,0,z) and B (5,1,-4) is,

Since P(0,0,z) is equidistant from the other two point.

So,

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