Given:

The point (1, 2, 3)

Distance = \( \sqrt{21}\)

We know x = 0 and y = 0 on z-axis

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

According to question:

RA = \( \sqrt{21}\)

RA^{2} = 21

By using the formula,

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

We know, RA^{2} = 21

5 + (z – 3)^{2} = 21

z^{2}+ 9 – 6z + 5 = 21

z^{2} – 6z = 21 – 14

z^{2}– 6z – 7 = 0

z^{2}– 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

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

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