Examples

Chapter 10 Class 12 Vector Algebra
Serial order wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Example 30 (Supplementary NCERT) Prove that [β 8(π β" + " π β&π β+π β&π β+π β )] = 2 [π β , π β, π β] Solving LHS [β 8(π β" + " π β&π β+π β&π β+π β )] = (π β" + " π β). ["(" π β+π β") " Γ " (" π β+π β)] = (π β" + " π β). ["(" π βΓπ β") + (" π βΓπ β)+"(" π βΓπ β") + (" π βΓπ β)] = "(" π β+π β")." [(π βΓπ β") + (" π βΓπ β ) "+ 0 + (" π β" Γ " π β") " ] = π β. (π β Γ π β) + π β.(π β Γ π β) + π β. (π β Γ π β) + π β.(π β Γ π β) + π β.(π β Γ π β) + π β.(π β Γ π β) = [π β", " π β", " π β ] + [π β", " π β", " π β ] + [π β", " π β", " π β ] + [π β", " π β", " π β ] + [π β", " π β", " π β ] + [π β", " π β", " π β ] π β Γ π β = |π β ||π β | sin 0 π Μ = 0 [π β", " π β", " π β ] = [π β", " π β", " π β ] = π β. (π β Γ π β) As (π β Γ π β) = 0 β = π β . 0 β = 0 Using Prop: [π β", " π β", " π β ] = 0 [π β", " π β", " π β ] = 0 [π β", " π β", " π β ] = 0 [π β", " π β", " π β ] = 0 = [π β", " π β", " π β ] + 0 + 0 + 0 + 0 + [π β", " π β", " π β ] = [π β", " π β", " π β ] + [π β", " π β", " π β ] = [π β", " π β", " π β ] + [π β", " π β", " π β ] = 2[π β", " π β", " π β ] = R.H.S Hence proved