he66666
  • he66666
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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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?
anonymous
  • anonymous
(1.5, .5, 0)
anonymous
  • anonymous
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)

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anonymous
  • anonymous
seems pretty messy
anonymous
  • anonymous
not really... some terms will cancel out
he66666
  • he66666
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.
he66666
  • he66666
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

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