Question

"Find an equation for the set of points P(x, y, z) that are equidistant from the points A(1, 2, 3) and B(4, 0, 1)."

Can some one help?

Answer 1

Wouldn't that be the plane passing through the midpoint of AB and having as its normal the direction vector of AB ??

midpoint of AB = (5/2, 1, 2)
direction vector AB = (3,-2,-2)

the the plane has equation
3x - 2y - 2z + C = 0
but (5/2,1,2) lies on it, so
15/2 - 2 - 4 + C = 0
C = -3/2

so 3x - 2y - 2z - 3/2 = 0 or
6x - 4y - 4z - 3 = 0