Find an equation of the set of all points equidistant from the points A(−3, 6, 3) and B(4, 1, −1). Describe the set.

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Step-by-step explanation:

I will describe this set in R³. Let P=(x,y,z) be a point equidistant to A and B, that is, the distance from P to A is equal to the distance from P to B.

First, using the usual distance formula, the distance from P to A is equal to

On the other hand, the distance form P to B is equal to

P is equidistant from A and B if and only if P satisfies the equation d(P,A)=d(P,B), that is,

Take the square in both sides of this equation to get

You can simplify using difference of squares and multiplying like this:

which is the equation of a plane.

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step-by-step explanation: