Miscellaneous

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

### Transcript

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_1βπ_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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.