Find an equation of the set of all points equidistant from the points A(-1, 6, 3) and B(5, 3, -3).

Question:

Find an equation of the set of all points equidistant from the points {eq}A(-1, 6, 3) {/eq} and {eq}B(5, 3, -3) {/eq}.

The Equation of a Plane:

To solve this problem, we need to compute the midpoint {eq}(P) {/eq} between them and the normal {eq}(n) {/eq} to the plane.

Next, we'll use {eq}P {/eq} and {eq}n {/eq} to write the equation of the plane.

Answer and Explanation:

We are given two points: {eq}A= (-1, 6, 3) , B= (5,3,-3) {/eq}

The plane contains the midpoint between the given points :

{eq}P= \left(...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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