Last updated at May 29, 2018 by Teachoo

Transcript

Ex 11.3, 11 Find the equation of the plane thro ugh the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x y + z = 0. Equation of a plane passing through the intersection of planes A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 (A1x + B1y + C1z d1) + (A2x + b2y + c2z d2) = 0 Given the planes passes through Equation of plane is ( 1 x + 1 y + 1 z = d1) + ( 2 x + 2 y + 2 z = d2) = 0 Putting values (1x + 1y + 1z 1) + (2x + 3y + 4z 5) = 0 x + y + z 1 + 2 x + 3 y + 4 z 5 = 0 (1 + 2 ) x + (1 + 3 )y + (1 + 4 ) z + ( 1 5 ) = 0 Also, the plane is perpendicular to the plane x y + z = 0 So, the normal vector to be the plane is perpendicular to the normal vector of x y + z = 0. Since, is perpendicular to , 1 2 + b1b2 + c1 c2 = 0 (1 + 2 ) 1 + (1 + 3 ) 1 + (1 + 4 ) 1 = 0 1 + 2 1 3 + 1 + 4 = 0 1 + 3 = 0 1 = 3 = Putting value of in (1), (1 + 2 ) x + (1 + 3 )y + (1 + 4 ) z + ( 1 5 ) = 0 1+2 1 3 x + 1+3 1 3 y + 1+4 1 3 z + 1 5 1 3 = 0 1 2 3 x + 1 1 y + 1 4 3 z + 1+ 5 3 = 0 1 3 x + 0y 1 3 z + 2 3 = 0 1 3 x 1 3 z + 2 3 = 0 1 3 (x z + 2) = 0 x z + 2 = 0 Therefore, the equation of the plane is x z + 2 = 0

Example, 3
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Ex 11.1, 2 Important

Example, 6 Important

Example, 9 Important

Example 12 Important

Ex 11.2, 5 Important

Ex 11.2, 11 Important

Ex 11.2, 12 Important

Ex 11.2, 14 Important

Ex 11.2, 15 Important

Ex 11.2, 17 Important

Example 20 Important

Example 21 Important

Example 23 Important

Example 24 Important

Example, 25 Important

Ex 11.3, 4 Important

Ex 11.3, 11 Important You are here

Ex 11.3, 12 Important

Ex 11.3, 14 Important

Example 27 Important

Example 29 Important

Example 30 Important

Misc 6 Important

Misc 9 Important

Misc 14 Important

Misc 18 Important

Misc 20 Important

Misc 21 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.