Equation of Plane
What is Plane?
A plane, in mathematics and geometry, refers to a flat, two-dimensional surface that extends infinitely in all directions.
What are the Different forms of Equations of Plane?
There are various forms of the equation of a plane, each serving different purposes. These forms include the general form, normal form, intercept form, and vector form.
What are the General Equation of Plane?
The general equation of a plane takes 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.
What is Intercept form of Equation of Plane?
Intercept form of the equation of a plane is expressed as x/a + y/b + z/c = 1, where a, b, and c are the intercepts of the plane on the x, y, and z axes respectively.
Write Equation of Plane in Vector Form.
Equation of plane in vector form is expressed as ([Tex]\vec{r} = \vec{r_0} + s\vec{v} + t\vec{w}[/Tex]), where ([Tex]\vec{r_0}[/Tex]) is the known point, ([Tex]\vec{v}[/Tex]) and ([Tex]\vec{w}[/Tex]) are the non-parallel vectors, and (s) and (t) are scalar parameters.
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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