Question -
Answer -
Given:
The point (1, 2, 3)
Distance = √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 = √21
RA2 = 21
By using the formula,
The distance between any two points (a, b, c) and (m, n, o)is given by,
We know, 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
∴The points(0, 0, 7) and (0, 0, -1) on z-axis is equidistant from (1, 2, 3).