Examples

Chapter 10 Class 12 Vector Algebra
Serial order wise

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Example 14 Find angle βΞΈβ 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+(β1)2) |π β | = β(1+1+1) = βπ Magnitude of π β = β(12+(β1)2+12) |π β | = β(1+1+1) = βπ 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.(β1) + (β1)1 = 1 β 1 β 1 = β1 Now, π β . π β = "|" π β"|" "|" π β"|" cos ΞΈ Putting values β1 = β3 Γ β3 Γ cos ΞΈ β1 = 3 cos ΞΈ cos ΞΈ = (β1)/3 ΞΈ = cosβ1 ((βπ)/π) Therefore, the angle between π β and π β is cos-1((β1)/3)