Last updated at May 6, 2021 by

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Example 27 If π Μ + π Μ + π Μ, 2π Μ + 5π Μ, 3π Μ + 2π Μ β 3π Μ and π Μ β 6π Μ β π Μ are the position vectors of points A, B, C and D respectively, then find the angle between (π΄π΅) β and (πΆπ·) β . Deduce that (π΄π΅) β and (πΆπ·) β are collinear.Angle between (π΄π΅) β & (πΆπ·) β is given by cos ΞΈ = ((π¨π©) β . (πͺπ«) β)/|(π¨π©) β ||(πͺπ«) β | A(π Μ + π Μ + π Μ), B(2π Μ + 5π Μ) (π¨π©) β = (2 β 1) π Μ + (5 β 1) π Μ + (0 β 1) π Μ = 1π Μ + 4π Μ β π Μ |(π¨π©) β | = β(1^2+4^2+(β1)^2 ) = β18 = β(9 Γ 2) = 3βπ C(3π Μ + 2π Μ β 3π Μ), D(π Μ β 6π Μ β π Μ) (πΆπ·) β = (1 β 3) π Μ + (β6 β 2) π Μ + (β1 β (-3)) π Μ = β2π Μ β 8π Μ + 2π Μ |(πͺπ«) β | = β((β2)^2+(β8)^2+2^2 ) = β72 = β(36 Γ 2) = 6βπ Now, cos ΞΈ = ((π¨π©) β . (πͺπ«) β)/|(π¨π©) β ||(πͺπ«) β | = ((π Μ + 4π Μ β π Μ ).(β2π Μ β 8π Μ + 2π Μ ))/(3β2 Γ 6β2) = (1(β2) + 4(β8) β 1(2))/(3β2 Γ 6β2) = (β2 β 32 β 2)/(3 Γ 6 Γ β2 Γ β2) = (β36)/36 = β1 Since cos ΞΈ = β1, ΞΈ = 180Β° So, ΞΈ = 180Β° = 180Β° Γ π/180 = Ο So, angle between (π΄π΅) β & (πΆπ·) β is Ο Also, Since angle between (π΄π΅) β & (πΆπ·) β is 180Β° , they are in opposite directions Since (π΄π΅) β & (πΆπ·) β are parallel to the same line π β, they are collinear.

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Example 26 (Supplementary NCERT) Deleted for CBSE Board 2022 Exams

Example 27 (Supplementary NCERT) Deleted for CBSE Board 2022 Exams

Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.