Chapter 11 Class 12 Three Dimensional Geometry
Ex 11.1, 2
Example, 6 Important
Example, 7
Example 10 Important
Ex 11.2, 5 Important
Ex 11.2, 9 (i) Important
Ex 11.2, 10 Important
Ex 11.2, 12 Important
Ex 11.2, 13 Important
Ex 11.2, 15 Important
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Question 11 Important Deleted for CBSE Board 2024 Exams
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Question 14 Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 4 (a) Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 12 Important Deleted for CBSE Board 2024 Exams
Question 14 (a) Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Question 19 Important Deleted for CBSE Board 2024 Exams
Question 20 Important Deleted for CBSE Board 2024 Exams
Misc 3 Important
Misc 4 Important
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 14 Important Deleted for CBSE Board 2024 Exams
Misc 5 Important
Question 16 Important Deleted for CBSE Board 2024 Exams You are here
Chapter 11 Class 12 Three Dimensional Geometry
Last updated at April 16, 2024 by Teachoo
Question 16 Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then 1/𝑎2 + 1/𝑏2 + 1/𝑐2 = 1/𝑝2 . Distance of the point (𝑥_1,𝑦_1,𝑧_1) from the plane Ax + By + Cz = D is |(𝑨𝒙_𝟏 + 𝑩𝒚_𝟏 + 𝑪𝒛_𝟏 − 𝑫)/√(𝑨^𝟐 + 𝑩^𝟐 + 𝑪^𝟐 )| The equation of a plane having intercepts 𝑎, b, c on the x −, y − & z − axis respectively is 𝒙/𝒂 + 𝒚/𝒃 + 𝒛/𝒄 = 1 Comparing with Ax + By + Cz = D, A = 1/𝑎 , B = 1/𝑏 , C = 1/𝑐 , D = 1 Given, the plane is at a distance of ‘𝑝’ units from the origin. So, The point is O(0, 0, 0) So, 𝑥_1 = 0, 𝑦_1= 0, 𝑧_1= 0 Now, Distance = |(𝐴𝑥_1 + 𝐵𝑦_1 + 𝐶𝑧_1 − 𝐷)/√(𝐴^2 + 𝐵^2 + 𝐶^2 )| Putting values 𝑝 = |(1/𝑎 × 0 + 1/𝑏 × 0 + 1/𝑐 × 0 − 1)/√((1/𝑎)^2+ (1/𝑏)^2+ (1/𝑐)^2 )| 𝑝 = |(0 + 0 + 0 − 1)/(√(1/𝑎^2 + 1/𝑏^2 + 1/𝑐^2 ) )| 𝑝 = |(−1)/(√(1/𝑎^2 + 1/𝑏^2 + 1/𝑐^2 ) )| 𝑝 = 1/(√(1/𝑎^2 + 1/𝑏^2 + 1/𝑐^2 ) ) 1/𝑝 = √(1/𝑎^2 + 1/𝑏^2 + 1/𝑐^2 ) Squaring both sides 1/𝑝^2 = 1/𝑎^2 + 1/𝑏^2 + 1/𝑐^2 Hence proved.