Chapter 10 Class 12 Vector Algebra
Concept wise

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Misc 7 If π β = π Μ + π Μ + π Μ, π β = 2π Μ βπ Μ + 3π Μ and π β = π Μ β 2π Μ + π Μ , find a unit vector parallel to the vector 2π β β π β + 3π β . Given π β = π Μ + π Μ + π Μ π β = 2π Μ + π Μ + 3π Μ π β = π Μ β 2π Μ + π Μ Let π β = 2π β β π β + 3π β = 2(π Μ + π Μ + π Μ) β (2π Μ β π Μ + 3π Μ) + 3(π Μ β2π Μ + π Μ) = 2π Μ + 2π Μ + 2π Μ β 2π Μ + 1π Μ β 3π Μ + 3π Μ β 6π Μ + 3π Μ = (2 β 2 + 3) π Μ + (2 + 1 β 6) π Μ + (2 β 3 + 3) π Μ = 3π Μ β 3π Μ + 2π Μ β΄ π β = 3π Μ β 3π Μ + 2π Μ Magnitude of π β = β(32+(β3)2+22) |π β | = β(9+9+4) = βππ Unit vector in the direction of π β = π/|π β | x π β = 1/β22 Γ [3π Μ β3π Μ+2π Μ ] = 3/β22 π Μ β 3/β22 π Μ + 2/β22 π Μ Hence the required vector is π/βππ π Μ β π/βππ π Μ + π/βππ π Μ