Equation Of Plane
Easymathematics
The general equation of a plane in 3D is
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Solution
Incorrect! Answer:
Ax + By + Cz + D = 0
- Definition: A plane is a surface such that if any two points are taken on it, the entire line segment joining them lies on the surface.
- Normal Vector: Any plane is uniquely determined by a point on it and a vector n=Ai^+Bj^+Ck^ normal to it.
- Derivation: For a point (x,y,z) on the plane passing through (x0,y0,z0): A(x−x0)+B(y−y0)+C(z−z0)=0⟹Ax+By+Cz−(Ax0+By0+Cz0)=0
- General Form: Letting D=−(Ax0+By0+Cz0), we get Ax+By+Cz+D=0.
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About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- equation of plane
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Ax + By + Cz + D = 0
- Definition: A plane is a surface such that if any two points are taken on it, the entire line segment joining them lies on the surface.
- Normal Vector: Any plane is uniquely determined by a point on it and a vector n=Ai^+Bj^+Ck^ normal to it.
- Derivation: For a point (x,y,z) on the plane passing through (x0,y0,z0): A(x−x0)+B(y−y0)+C(z−z0)=0⟹Ax+By+Cz−(Ax0+By0+Cz0)=0
- General Form: Letting D=−(Ax0+By0+Cz0), we get Ax+By+Cz+D=0.
This easy difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of equation of plane. It appeared in the 2025 exam.
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