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Last updated at Feb. 4, 2020 by Teachoo

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Misc 2 If π_1 , π_1, π_1 and π_2 , π_2, π_2 are the direction cosines of two mutually perpendicular lines, show that direction cosines of line perpendicular to both of these are π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1.We know that π β Γ π β is perpendicular to both π β & π β So, required line is cross product of lines having direction cosines π_1 , π_1, π_1 and π_2 , π_2, π_2 Required line = |β 8(π Μ&π Μ&π Μ@π_1&π_1&π_1@π_2&π_2&π_2 )| = π Μ (π_1 π_2 β π_2 π_1) β π Μ (π_1 π_2 β π_2 π_1) + π Μ(π_1 π_2 β π_2 π_1) = (π_1 π_2 β π_2 π_1) π Μ + (π_2 π_1βπ_1 π_2) π Μ + (π_1 π_2 β π_2 π_1) π Μ Hence, direction cosines = π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1 β΄ Direction cosines of the line perpendicular to both of these are π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1 , π_1 π_2 β π_2 π_1. Hence proved

Miscellaneous

Misc 1
Important

Misc 2 You are here

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

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.