Find the points on z-axis which are at a distance 
from the point (1, 2, 3).
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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