Examples

Chapter 10 Class 12 Vector Algebra
Serial order wise

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

### Transcript

Example 28 (Supplementary NCERT) Find π if the vectors π β = π Μ + 3π Μ + π Μ, π β = 2π Μ β π Μ β π Μ and π β = ππ Μ + 7π Μ + 3π Μ are coplanar.Three vectors π β, π β, π β are coplanar if [π β" " π β" " π β ] = 0 Given, π β = π Μ + 3π Μ + π Μ π β = 2π Μ β π Μ β π Μ π β = Ξ»π Μ + 7π Μ + 3π Μ [π β" " π β" " π β ] = |β 8(1&3&[email protected]&β1&β1@π&7&3)| 0 = 1[(β1Γ3)β(7Γβ1) ] β 3[(2Γ3)β(Ξ»Γβ1) ] + 1[(2Γ7)β(Ξ»Γβ1) ] 0 = 1 [β3β(β7)]β3[6β(βΞ»)]+1[14β(βΞ»)] 0 = 1 [β3+7]β3[6+Ξ»]+1[14+Ξ»] 0 = 4 β 18 β 3Ξ» + 14 + Ξ» 0 = 18 β 18 β 3Ξ» + Ξ» 0 = β 2Ξ» β2Ξ» = 0 Ξ» = 0/(β2) π = 0 Therefore, π β,π,π β are coplanar if Ξ» = 0