Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).

Given: Points are A(3, 1, 2) and B(5, 5, 2)

To find: the point on y-axis which is equidistant from the points

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

Let R(0, y, 0) any point on the y-axis

According to the question:

RA = RB

⇒ RA² = RB²

Formula used:

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

Therefore,

The distance between R(0, y, 0) and A(3, 1, 2) is RA,

Distance between R(0, y, 0) and B(5, 5, 2) is RB,

As RA² = RB²

13+ (y – 1)² = (y – 5)² + 29

⇒ y²+ 1 – 2y + 13 = y²+ 25 – 10y + 29

⇒ 10y – 2y = 54 – 14

⇒ 8y = 40

⇒ y = 5

Hence point R(0, 5, 0) on y-axis is equidistant from (3, 1, 2) and (5, 5, 2)