Cartesian Form of Equation of a Plane
The point-normal form equation of a plane:
[Tex]\vec{n} \cdot (\vec{r} – \vec{r_0}) = 0[/Tex]
Where ( [Tex]\vec{n}[/Tex] = ❬a,b,c❭) is the normal vector to the plane, ( [Tex]\vec{r_0}[/Tex] = ❬ x0, y0, z0 ❭ ) is a known point on the plane, and ( [Tex]\vec{r} [/Tex]= ❬x,y,z❭) represents any point on the plane.
Expanding the dot product, we get:
a(x – x0) + b(y – y0) + c(z – z0) = 0
This equation can be rearranged to obtain the Cartesian form of the equation of the plane:
ax + by + cz = ax0 + by0 + cz0
Thus, the Cartesian form of the equation of a plane is:
ax + by + cz = d
where ( d = ax0 + by0 + cz0) is a constant.
Read More about Coordinate Axes and Planes in 3D Space.
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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