Miscellaneous
Misc 2 Important
Misc 3 Important
Misc 4 Important
Misc 5 Important
Question 1 Important
Question 2 You are here
Question 3 Important
Question 4
Question 5 Important
Question 6
Question 7 Important
Question 8 Important
Question 9 Important
Question 10 Important
Question 11 Important
Question 12
Question 13 Important
Question 14 Important
Question 15
Question 16 Important
Question 17 (MCQ) Important
Question 18 (MCQ) Important
Miscellaneous
Last updated at April 16, 2024 by Teachoo
Question 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