CBSE Class 12 Sample Paper for 2019 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 10 (OR 2 nd question)

Find the angle between the vectors:

Β  a = i + j β k and b = i β j + k

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Question 10 (OR 2nd question) Find the angle 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 and 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 & π β Now, π β. π β = (π Μ + π Μ β π Μ). (π Μ β π Μ + π Μ) = (1π Μ + 1π Μ β π Μ). (1π Μ β 1π Μ + 1π Μ) = 1 Γ 1 + 1 Γ (β1) + (-1) Γ 1 = 1 β 1 β 1 = β1 Magnitude of π β = β(12+12+(β1)2) |π β |= β(1+1+1) = β3 Magnitude of π β = β(12+(β1)2+12) |π β |= β(1+1+1) = β3 Now, π β . π β = |π β ||π β | cos ΞΈ β1 = β3 Γ β3 Γ cos ΞΈ β1 = 3 cos ΞΈ cos ΞΈ = (β1)/3 ΞΈ = πππ^(βπ) ((βπ)/π) Thus, the angle between π β and π β is cos-1((βπ)/π)