Last updated at May 6, 2021 by
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Ex 10.5, 3 (Supplementary NCERT) Find π if the vectors π Μ β π Μ + π Μ, 3π Μ + π Μ + 2π Μ and π Μ + ππ Μ β 3π Μ are coplanar.Three vectors π β, π β, π β are coplanar if [π β" " π β" " π β ] = 0 Let π β = π Μ β π Μ + π Μ π β = 3π Μ + π Μ + 2π Μ π β = π Μ + ππ Μ β 3π Μ Now, [π β" " π β" " π β ] = |β 8(1&β1&1@3&1&2@1&"π" &β3)| 0 = 1[(1Γβ3)β("π" Γ2) ] β (β1)[(3Γβ3)β(1Γ2) ] + 1[(3Γ"π" )β(1Γ1) ] 0 = 1 [β3β2"π" ]+1[β9β2]+1[3"π" β1] 0 = β3 β 2π β 11 + 3π β 1 0 = β3 β 11 β 1 + 3π β 2Ξ» 0 = β15 + π 15 = Ξ» π = 15 Therefore, π β,π,π β are coplanar if Ξ» = 15
Ex 10.5 (Supplementary NCERT)
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Ex 10.5 (Supplementary NCERT)
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