Question

Find an equation for the plane consisting of all points that are equidistant from the points (-4,2,1) and (2,-4,3).

Answer 1

do you remember the distance formula in 3-dimensions?

Answer 2

Let the set of all points that are EQUIDISTANT from those two points be (x, y, z).
Now you can set up an equation relating their distances:
let:
\(\huge D_1=\sqrt{(x-(-4))^2+(y-2)^2+(z-1)^2} \)
\(\huge D_2=\sqrt{(x-2))^2+(y+4)^2+(z-3)^2} \)
now set \(\huge D_1 = D_2 \) and simplify...