Find an equation of the plane. The plane through the origin and the points (2, -4, 6) and (5, 1, 3).

Question:

Find an equation of the plane.

The plane through the origin and the points {eq}(2, -4, 6) {/eq} and {eq}(5, 1, 3) {/eq}.

The Equation of the Plane:

In this problem, we need to find out the equation of the plane passes through the origin and the given points.

So we'll use the fact that the direction of the normal to the plane will be perpendicular to the given two vectors. So we'll find out {eq}\vec{p}= \vec{n_1} \times \vec{n_2} {/eq} and plug in {eq}d=0 {/eq} to get the desired solution.

Answer and Explanation:

We are given two points of the plane {eq}(2, -4, 6) {/eq} and {eq}(5, 1, 3) {/eq}.

The direction of the normal to the plane will be perpendicular...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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