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Last updated at Feb. 1, 2020 by Teachoo

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Misc 22 (Method 1) Distance between two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is (A) 2 units (B) 4 units (C) 8 units (D) 2/โ29 units Distance between two parallel planes Ax + By + Cz = ๐_1 and Ax + By + Cz = ๐_2 is |(๐ _๐ โ ๐ _๐)/(โ(๐จ^๐ + ๐ฉ^๐ + ๐ช^๐ ) )| 2x + 3y + 4z = 4 Comparing with Ax + By + Cz = d1 A = 2, B = 3, C = 4, d1 = 4 4x + 6y + 8z = 12 2 (2x + 3y + 4z) = 12 Dividing by 2 2x + 3y + 4z = 6 Comparing with Ax + By + Cz = d2 A = 2, B = 3, C = 4 , d2 = 6 So, Distance between the two planes = |(4 โ 6)/โ(2^2 + 3^2 + 4^2 )| = |(โ2)/โ(4 + 9 + 16)| = ๐/โ๐๐ Hence, (D) is the correct option Misc 22 (Method 2) Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is (A) 2 units (B) 4 units (C) 8 units (D)2/โ29 units Distance of a point (๐ฅ_1, ๐ฆ_1, ๐ง_1) from the plane Ax + By + Cz = D is |(๐จ๐_๐ + ๐ฉ๐_๐ + ๐ช๐_๐โ ๐ซ)/โ(๐จ^๐ + ๐ฉ^๐ + ๐ช^๐ )| Let us take a point P (๐ฅ_1, ๐ฆ_1, ๐ง_1) on the plane 2x + 3y + 4z = 4 2๐ฅ_1 + 3๐ฆ_1 + 4๐ง_1 = 4 Now, to find the distance of point P form plane 4x + 6y + 8z = 12, Comparing with Ax + By + Cz = D, A = 4, B = 6, C = 8, D = 12 Distance of P (๐ฅ_1, ๐ฆ_1, ๐ง_1) from the plane 4x + 6y + 8z = 12 = |(4๐ฅ_1+ ใ6๐ฆใ_1 + 8๐ง_1โ 12)/โ(4^2 + 6^2 + 8^2 )| = |(2(๐๐_๐ + ใ๐๐ใ_๐ + ๐๐_๐ )โ 12)/โ(16 + 36 + 64)| = |(2 ร ๐ โ 12)/โ116| = |(8 โ 12)/โ(4 ร 29)| = |(โ4)/(2โ29)| = ๐/โ๐๐ Hence, (D) is the correct option

Miscellaneous

Misc 1
Important

Misc 2

Misc 3 Not in Syllabus - CBSE Exams 2021

Misc 4 Important

Misc 5 Important Not in Syllabus - CBSE Exams 2021

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22 Important You are here

Misc 23 Important

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.