Find the equation of the set of points which are equidistant from the points `(1,2,3)` and `(3,2,-1)`

Answer

N/a

Explanation

Let required point be `P-=(x,y,z)`.
Let given points are `A-=(1,2,3) " and" B-=(3,2,-1)`.
Given that, PA=PB
`implies PA^(2)=PB^(2)`
`implies (x-1)^(2)+(y-2)^(2)+(z-3)^(2)+(y-2)^(2)+(z+1)^(2)`
`implies (x-1)^(2)+(z-3)^(2)=(x-3)^(2)+(z+1)^(2)`
`implies x^(2)-2x+1+z^(2)-6x+9+z^(2)+2z+1`
`implies 4x-8z=0`
`implies z-2x=0`
Which is the equation of set of points p.