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Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2023 Exams
Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2023 Exams
Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2023 Exams
Last updated at March 30, 2023 by Teachoo
Example 21 (Introduction) Show that the points A(β2π Μ + 3π Μ + 5π Μ), B(π Μ + 2π Μ + 3π Μ) and C(7π Μ β π Μ) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three position vectors collinear i.e. |(π΄π΅) β | + |(π΅πΆ) β | = |(π΄πΆ) β | Example 21 Show that the points A(β2π Μ + 3π Μ + 5π Μ), B(π Μ + 2π Μ + 3π Μ) and C(7π Μ β π Μ) are collinear. Given A (β2π Μ + 3π Μ + 5π Μ) B (1π Μ + 2π Μ + 3π Μ) C (7π Μ + 0π Μ β 1π Μ) 3 points A, B, C are collinear if |(π¨π©) β | + |(π©πͺ) β | = |(π¨πͺ) β | Finding (π¨π©) β , (π©πͺ) β , (π¨πͺ) β (π¨π©) β = (1 β (-2)) π Μ + (2 β 3) π Μ + (3 β 5) π Μ = 3π Μ β 1π Μ β 2π Μ (π©πͺ) β = (7 β 1) π Μ + (0 β 2) π Μ + (-1β3) π Μ = 6π Μ β 2π Μ β 4π Μ (π¨πͺ) β = (7 β (-2)) π Μ + (0 β 3) π Μ + (-1 β 5) π Μ = 9π Μ β 3π Μ β 6π Μ Magnitude of |(π΄π΅) β | = β(3^2+(β1)^2+(β2)^2 ) |(π¨π©) β | = β(9+1+4) = βππ Magnitude of |(π΅πΆ) β | = β(6^2+(β2)^2+(β4)^2 ) |(π©πͺ) β | = β(36+4+16) = β56 = β(4 Γ 14) = 2βππ Magnitude of |(π΄πΆ) β | = β(9^2+(β3)^2+(β6)^2 ) |(π¨πͺ) β | = β(81+9+36) = β126 = β(9 Γ 14) = 3βππ Thus, |(π¨π©) β | + |(π©πͺ) β | = β14 + 2β14 = 3β14 = |(π¨πͺ) β | Thus, A, B and C are collinear.