Question -
Answer -
Given:
The point (1, 2, 3)
Distance = тИЪ21┬а
We know x = 0 and y = 0 on z-axis
Let R(0, 0, z) any point on z-axis
According to question:
RA = тИЪ21┬а
RA2┬а= 21
By using the formula,
The distance┬аbetween any two points (a, b, c) and (m, n, o)is given by,
We know, RA2┬а= 21
5 + (z тАУ 3)2┬а= 21
z2+ 9 тАУ 6z + 5 = 21
z2┬атАУ 6z = 21 тАУ 14
z2тАУ 6z тАУ 7 = 0
z2тАУ 7z + z тАУ 7 = 0
z(zтАУ 7) + 1(z тАУ 7) = 0
(zтАУ 7) (z + 1) = 0
(zтАУ 7) = 0 or (z + 1) = 0
z= 7 or z = -1
тИ┤The┬аpoints(0, 0, 7) and (0, 0, -1)┬аon z-axis is equidistant from┬а(1, 2, 3).