calc 3

Question
Find an equation of the set of all points equidistant from the points
A(−2, 5, 2) and B(5, 1, −3).

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asked by Becky
  1. Think of two points in space.

    The set of all points equidistant from the points is therefore a plane that separates the two points, right in the middle.

    Also the line joining the two points would be perpendicular to the plane.

    The mid-point between the two points would evidently lie on the plane.

    (1) Find the mid-point between the two given points using the mid-point formula. Let this be p0.
    (2) Find the vector AB joining the two given points. Then AB is the normal vector to the plane we're looking for.
    Let AB=<a,b,c>
    (3) Use the components of the normal vector AB (a,b,c) to form the equation of the required plane:
    a(x-x0)+b(y-y0)+c(z-z0)=0
    where (x0,y0,z0) is the mid-point P0 between A and B.

    If you need more details, please post.

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