

Get live Maths 1-on-1 Classs - Class 6 to 12
Miscellaneous
Misc 2 You are here
Misc 3
Misc 4 Important
Misc 5 Important
Misc 6 Important
Misc 7 Deleted for CBSE Board 2023 Exams
Misc 8 Important Deleted for CBSE Board 2023 Exams
Misc 9 Important
Misc 10 Deleted for CBSE Board 2023 Exams
Misc 11 Important Deleted for CBSE Board 2023 Exams
Misc 12 Important Deleted for CBSE Board 2023 Exams
Misc 13 Important Deleted for CBSE Board 2023 Exams
Misc 14 Important Deleted for CBSE Board 2023 Exams
Misc 15 Important Deleted for CBSE Board 2023 Exams
Misc 16 Deleted for CBSE Board 2023 Exams
Misc 17 Important Deleted for CBSE Board 2023 Exams
Misc 18 Important Deleted for CBSE Board 2023 Exams
Misc 19 Deleted for CBSE Board 2023 Exams
Misc 20 Important
Misc 21 Important Deleted for CBSE Board 2023 Exams
Misc 22 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 23 (MCQ) Important Deleted for CBSE Board 2023 Exams
Miscellaneous
Last updated at March 16, 2023 by Teachoo
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[email protected]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