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Question 9 - Equation of plane - Intercept Form - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at April 16, 2024 by Teachoo
Equation of plane - Intercept Form
Chapter 11 Class 12 Three Dimensional Geometry
Concept wise
- Direction cosines and ratios
- Equation of line - given point and //vector
- Equation of line - given 2 points
- Angle between two lines - Vector
- Angle between two lines - Cartisian
- Angle between two lines - Direction ratios or cosines
- Shortest distance between two skew lines
- Shortest distance between two parallel lines
- Equation of plane - In Normal Form
- Equation of plane - Prependicular to Vector & Passing Through Point
- Equation of plane - Passing Through 3 Non Collinear Points
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Equation of plane - Intercept Form
- Equation of plane - Passing Through Intersection Of Planes
- Coplanarity of 2 lines
- Angle between two planes
- Distance of point from plane
- Angle between Line and Plane
- Equation of line under planes condition
- Point with Lines and Planes
Transcript
Question 9 Find the equation of the plane with intercepts 2, 3 and 4 on the x, y and z-axis respectively. The equation of a plane with intercepts 𝑎, b, c on x, y, and z – axis respectively is 𝒙/𝒂 + 𝒚/𝒃 + 𝒛/𝒄 = 1 Given, Intercept on x − axis = 2 ∴ 𝑎 = 2 Intercept on y − axis = 3 ∴ b = 3 Intercept on z – axis = 4 ∴ c = 4 Equation of plane is 𝒙/𝟐 + 𝒚/𝟑 + 𝒛/𝟒 = 1 6𝑥/12 + 4𝑦/12 + 3𝑧/12 = 1 (6𝑥 + 4𝑦 + 3𝑧)/12 = 1 6x + 4y + 3z = 12
