Answer :

Given: Points A(1, 2, 3)


To find: the point on z-axis which is at distance of from the given point


As we know x = 0 and y = 0 on z-axis


Let R(0, 0, z) any point on z-axis


According to question:



RA2 = 21


Formula used:


The distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


Distance between R(0, 0, z) and A(1, 2, 3) is RA,





As RA2 = 21


5 + (z – 3)2 = 21


z2+ 9 – 6z + 5 = 21


z2 – 6z = 21 – 14


z2– 6z – 7 = 0


z2– 7z + z – 7 = 0


z(z– 7) + 1(z – 7) = 0


(z– 7) (z + 1) = 0


(z– 7) = 0 or (z + 1) = 0


z= 7 or z = -1


Hence points (0, 0, 7) and (0, 0, -1) on z-axis is equidistant from (1, 2, 3)


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