https://math.stackexchange.com › ... › 2686606 › equation-of-a-plane-passing-through-3-points

Get two different vectors which are in the plane, such as $B-A=(3,0,-3)$ and $C-A=(3,3,3)$. Compute the cross product of the two obtained vectors: $(B-A)×(C-A)=(9,-18,9)$. This is the normal vector of the plane, so we can divide it by 9 and get $(1,-2,1)$.

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This Calculus 3 video tutorial explains how to find the equation of a plane given three points.Area - Vector Cross Product: https://www.youtub...

https://www.wolframalpha.com › widgets › view.jsp

Plane Through Three Points. It is enough to specify tree non-collinear points in 3D space to construct a plane. Equation, plot, and normal vector of the plane are calculated given x, y, z coordinates of tree points.

https://planetcalc.com › 8243

A plane can be uniquely determined by three non-collinear points (points not on a single line). And this is what the calculator below does. You enter coordinates of three points, and the calculator calculates the equation of a plane passing through three points.

https://en.wikipedia.org › wiki › Euclidean_planes_in_three-dimensional_space

The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line.

https://math.libretexts.org › Bookshelves › Calculus › CLP-3_Multivariable_Calculus_(Feldman...

Find the equation of the plane containing the points \((1,0,1)\text{,}\) \((1,1,0)\) and \((0,1,1)\text{.}\) Is the point \((1,1,1)\) on the plane? Is the origin on the plane? Is the point \((4,-1,-1)\) on the plane?

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How do we find an equation of the plane passing through 3 points?In general, when we want to find an equation of a plane, we need to know a point lying in th...

https://www.contemporarycalculus.com › dh › Calculus_all › CC11_6_LinePlanes3D.pdf

In this section we examine the equations of lines and planes and their graphs in 3–dimensional space, discuss how to determine their equations from information known about them, and look at ways to determine intersections, distances, and angles in three dimensions.