Methods to Find Equation of a Plane
There are several methods to find the equation of a plane, each depending on the available information about the plane.
- The equation of a plane at a distance (d) from the origin with a unit normal vector ( [Tex]\hat{n} [/Tex]) is given by ( [Tex]\vec{r} \cdot \hat{n} = d [/Tex]).
- If a plane is perpendicular to a given vector ( [Tex]\vec{N}[/Tex] ) and passes through a point ( [Tex]\vec{a}[/Tex] ), its equation is ( [Tex](\vec{r} – \vec{a}) \cdot \vec{N} [/Tex]= 0 ).
- When a plane passes through three non-collinear points ( [Tex]\vec{a} [/Tex]), ( [Tex]\vec{b} [/Tex]), and ( [Tex]\vec{c}[/Tex]), its equation is given by ([Tex] (\vec{r} – \vec{a}) \cdot [(\vec{b} – \vec{a}) \times (\vec{c} – \vec{a})] [/Tex]= 0).
- If a plane passes through the intersection of two planes with normal vectors ( [Tex]\vec{n}_1[/Tex]) and ( [Tex]\vec{n}_2 [/Tex]) at distances ( d1 ) and ( d2 ) from the origin respectively, its equation is ( [Tex]\vec{r} \cdot (\vec{n}_1 + \lambda \vec{n}_2) = d_1 + \lambda d_2 [/Tex]).
Equation of Plane
Equation of Plane describes its position and orientation in three-dimensional space, typically represented in the form (ax + by + cz + d = 0), where (a), (b), and (c) are coefficients representing the plane’s normal vector, and (d) is the distance from the origin along the normal vector.
In this article, we will learn about the what is the equation of a plane, its definition and general form the equation, the equation of a plane in 3D Space, a Cartesian form of an equation of a plane, the equation of a plane in intercept and parametric form, etc. At the end of this article, you will see some examples of solved problems that will provide a better understanding of the topic.
Table of Content
- What is the Equation of Plane?
- General Form of Equation of a Plane
- Equation of a Plane in Three Dimensional Space
- Methods to Find Equation of a Plane
- Equation of a Plane in Normal Form
- Equation of a Plane Passing Through Three Points
- Cartesian Form of Equation of a Plane
- Equation of a Plane in Parametric Form
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