Find an equation of the set of all points equidistant from the points a(−3, 4, 3) and b(6, 1, −2). describe the set.

Let

P-------> the set of points equally distant from the two given points

we know that

Distance formula in three dimensions for the distance  between two points is equal to

P(x,y,z) A(-3,4,3) B(6,1,-2)

in this problem

1) Find the distance AP

2) Find the distance BP

3) Equate distance AP and distance BP

This is a plane, equidistant from each of A and B, which is perpendicular

to the line which joins A and B

therefore

the answer is

The equation is equal to

if x = 1, then the answer is 3.5

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step-by-step explanation: