(1) Write the (square of) distance from (x, y, z) to A(2, -1, 3).
(2) Write the (square of) distance from (x, y, z) to B(1, 2, -3).
(3) Equate (1) and (2).
Hi I'm stuck on the following questions:
a) Find an equation to describe the set of points equidistant from A(2, -1, 3) and B(1, 2, -3).
b) Find the coordinates of two points that are equidistant from A and B.
Please show the steps and thanks for your help!
I did PA = (2, -1, 3) - (x,y,z)
= (2-x, -1-y, 3-z)
PB = (1,2,-3) - (x,y,z)
= (1-x, 2-y, -3-z)
|PA| = |PB|
sqrt[(2-x)^2 + (-1-y)^2 + (3-z)^2] = sqrt[(1-x)^2 + (2-y)^2 + (-3-z)^2]
4 - 4x + x^2 + 1 + 2y + y^2 + 9 - 6z + z^2 = 1 - 2x + x^2 + 4 - 4y + y^2 + 9 +6z + z^2
-2x + 6y - 12z = 0
(sorry i'm not sure how to add the direction arrows)