Find the locus of the points which are equidistant from the points (1,2,3) and (3,2,11).

Explanation

Given points are `A(1,2,3) and B(3,2,11)`
We have to seek out the locus of the points which are equally distance from the points `A and B `
let point `P(x,y,z)` be a point that is in equal distance from `A and B`
so, `AP=BP`
`AP^2=BP^2`
`=>(x-1)^2+(y-2)^2+(z-3)^2=(x-3)^2+(y-2)^2+(z-11)^2`
`=>x^2+1-2x+y^2+4-4y+z^2+9-6z=x^2+9-6x+y^2+4-4y+z^2+121-22z`
`=>4x+16z+1-121=0`
`=>4x+16z-120=0`
`=>x+4z=30`
locus of that point is `x+4z=30`