# Find an equation for the plane consisting of all points that are equidistant from the points (-6,...

## Question:

Find an equation for the plane consisting of all points that are equidistant from the points {eq}(-6, \; 2, \; 3) {/eq} and {eq}(2, \; 4, \; 7) {/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.

We are given two points: {eq}(-6, 2, 3) , (2, 4, 7) {/eq}

The plane contains the midpoint between the given points :

{eq}P= \left( \dfrac{2+6}{2},...

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