Question

Grade 12 math: vectors?

Find the coordinates of two points that are equidistant from A(2, -1, 3) and B(1, 2, -3).

answer: (0, 0, 0) and (1, 1/2, 0)

how are you supposed to find the points? I found the equation that describes the set of points equidistant from A and B, which is x-3y+6z=0, but I don't know how to find the points.

Answer 1

We know that they are equidistant from the origin (0,0,0) because a^2+b^2+c^2 = z^2 gives the same result for each. Would the midpoint formula be a short cut here?

Answer 2

(1.5, .5, 0)

Answer 3

I would use distance formula:
d^2 = (x-2)^2 + (y+1)^2 + (z-3)^2 = (x-1)^2+(y-2)^2 + (z+3)^2
solve it & you get your point(s)

Answer 4

seems pretty messy

Answer 5

not really... some terms will cancel out

Answer 6

So I just use the distance formula? I thought there were many answers to this.. like I thought you could just plug in any number in x or y or z of the equation and solve for the others.

Answer 7

It doesn't work.. I ended up getting the same equation as my answer: -2x+6y-12z=0, which would be x-3y+6z=0