Practice Questions: Equation of Plane
Q1: Find the equation of the plane passing through the point (2, -1, 3) and perpendicular to the line with direction vector (❬ 1, 2, -3❭).
Q2: Determine the equation of the plane passing through the point (-1, 4, 2) and parallel to the plane with equation (2x – y + 3z = 5).
Q3: Find the equation of the plane passing through the points (-3, 1, 0), (1, 2, 3), and (2, -1, 4).
Q4: Determine the equation of the plane passing through the line of intersection of the planes (x – y + 2z = 3) and (2x + y – z = 1), and parallel to the plane (3x + 2y + 4z = 5).
Q5: Find the equation of the plane passing through the origin and containing the lines given by the parametric equations: (x = 2t – 1), (y = 3t + 2), (z = t + 4), and (x = t + 1), (y = 2t – 3), (z = 3t + 5).
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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