Answer :

Consider, C(0,0,z) point which lies on z axis and is equidistant from points A(1, 5, 7) and B(5, 1, -4).


AC = BC



Squaring both sides,


=


1 +25+ z2 -14z +49 = 25 + 1 + z2 +8z +16


-22z = -33


Z = 1.5


The point C is (0,0,1.5).


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