find the equation of the set of points which are equidistant from the points (1,2,3) and (3,2,-1).
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Answered by
27
consider(x,y,z) is any point in that plane
so,
(x-1)²+(y-2)²+(z-3)²=(x-3)²+(y-2)²+(z+1)²
x²+y²+z²-2x-4y-6z+1+4+9 = x²+y²+z²-6x-4y+2z+9+4+1
4x-8z=0
x=2z is the plane of all point equidistance
so,
(x-1)²+(y-2)²+(z-3)²=(x-3)²+(y-2)²+(z+1)²
x²+y²+z²-2x-4y-6z+1+4+9 = x²+y²+z²-6x-4y+2z+9+4+1
4x-8z=0
x=2z is the plane of all point equidistance
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