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Question -

Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, -4)



Answer -

Given:
The points (1, 5, 7) and (5, 1, -4)
We know x = 0 and y = 0 on z-axis
Let R(0, 0, z) any point on z-axis
According to the question:
RA = RB
RA2 = RB2
By using the formula,
The distance between any two points (a, b, c) and (m, n, o) is given by,

We know, RA2 = RB2

26+ (z – 7)2 = (z + 4)2 + 26

z2+ 49 – 14z + 26 = z2+ 16 + 8z + 26

49 – 14z = 16 + 8z

49 – 16 = 14z + 8z

22z = 33

z = 33/22

= 3/2

Thepoint R (0, 0, 3/2) on z-axis is equidistant from (1, 5, 7) and (5, 1,-4).

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