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Example 26 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams

Example 27 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams

Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Last updated at April 16, 2024 by Teachoo

Example 14 Find angle βΞΈβ between the vectors π β = π Μ + π Μ β π Μ and π β = π Μ β π Μ + π Μ. Given π β = π Μ + π Μ β π Μ π β = π Μ β π Μ + π Μ We know that π β . π β = "|" π β"|" "|" π β"|" cos ΞΈ where ΞΈ is the angle between π β and π β Finding |π β |, |π β | and π β . π β Magnitude of π β = β(12+1^2+(β1)2) |π β | = β(1+1+1) = βπ Magnitude of π β = β(12+(β1)2+12) |π β | = β(1+1+1) = βπ Finding π β . π β π β . π β = (1π Μ + 1π Μ β 1π Μ). (1π Μ β 1π Μ + 1π Μ) = 1.1 + 1.(β1) + (β1)1 = 1 β 1 β 1 = β1 Now, π β . π β = "|" π β"|" "|" π β"|" cos ΞΈ Putting values β1 = β3 Γ β3 Γ cos ΞΈ β1 = 3 cos ΞΈ cos ΞΈ = (β1)/3 ΞΈ = cosβ1 ((βπ)/π) Therefore, the angle between π β and π β is cos-1((β1)/3)