
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
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Example 26 (Supplementary NCERT) Deleted for CBSE Board 2024 Exams
Example 27 (Supplementary NCERT) Deleted for CBSE Board 2024 Exams
Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams You are here
Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Last updated at May 29, 2023 by Teachoo
Example 29 (Supplementary NCERT) Show that the four points A, B, C and D with position vectors 4π Μ + 5π Μ + π Μ, β(π Μ + π Μ), 3π Μ + 9π Μ + 4π Μ & β4π Μ + 4π Μ + 4π Μ, respectively coplanar Four points A, B, C, D are coplanar if the three vectors (π΄π΅) β , (π΄πΆ) β and (π΄π·) β are coplanar. i.e. [(π¨π©) β, (π¨πͺ) β, (π¨π«) β ] = 0 A (4π Μ + 5π Μ + π Μ) B (βπ Μ β π Μ) (π¨π©) β = (0π Μ β π Μ β π Μ) β (4π Μ + 5π Μ + π Μ) = β4π Μ β 6π Μ β 2π Μ A (4π Μ + 5π Μ + π Μ) C (3π Μ + 9π Μ + 4π Μ) (π¨πͺ) β = (3π Μ + 9π Μ + 4π Μ) β (4π Μ + 5π Μ + π Μ) = βπ Μ + 4π Μ + 3π Μ A (4π Μ + 5π Μ + π Μ) D (β4π Μ + 4π Μ + 4π Μ) (π¨π«) β = (β4π Μ + 4π Μ + 4π Μ) β (4π Μ + 5π Μ + π Μ) = β8π Μ β π Μ + 3π Μ [(π΄π΅) β, (π΄πΆ) β, (π΄π·) β ] = |β 8(β4&β6&β2@β1&4&3@β8&β1&3)| = β4[(4Γ3)β(β1Γ3) ] β (β6) [(β1Γ3)β(β8Γ3)] + (β2)[(β1Γβ1)β(β8Γ4) ] = β4 [12+3]+6[β3+24]β2[1+32] = β4 (15) + 6 (21) β 2 (33) = β60 + 126 β 66 = β126+ 126 = 0 β΄[(π΄π΅) β, (π΄πΆ) β, (π΄π·) β ] = 0 Therefore, points A, B, C and D are coplanar.