Ex 10.5 (Supplementary NCERT)

Chapter 10 Class 12 Vector Algebra
Serial order wise

This question is the same as Example 27 (Supplementary NCERT)

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### Transcript

Ex 10.5, 2 (Supplementary NCERT) Show that the vectors π β = π Μ β 2π Μ + 3π Μ, π β = β2π Μ + 3π Μ β 4π Μ and π β = π Μ β 3π Μ + 5π Μ are coplanarThree vectors π β, π β, π β are coplanar if [π β" " π β" " π β ] = 0 Given, π β = π Μ β 2π Μ + 3π Μ π β = β2π Μ + 3π Μ β 4π Μ π β = π Μ β 3π Μ + Ξ»π Μ Now, [π β" " π β" " π β ] = |β 8(1&β2&[email protected]β2&3&β[email protected]&β3&5)| = 1[(3Γ5)β(β3Γβ4) ] β (β2) [(β2Γ5)β(1Γβ4) ] + 3[(β2Γβ3)β(1Γ3) ] = 1 [15β(3 Γ4)]+2[β10β(β4)]+3[(2 Γ3)β3] = 1 [15β12]+2[β10+4]+3[6β3] = 1 [3]+2[β6]+3[3] = 3 β 12 + 9 = 0 Since [π β" " π β" " π β ] = 0 Vectors π β, π β, π β are coplanar