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Example 28 (Supplementary NCERT) - Find lambda if a = i + 3j +k, b = 2

Example 28 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2


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Example 28 (Supplementary NCERT) Find πœ† if the vectors π‘Ž βƒ— = 𝑖 Μ‚ + 3𝑗 Μ‚ + π‘˜ Μ‚, 𝑏 βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ βˆ’ π‘˜ Μ‚ and 𝑐 βƒ— = πœ†π‘– Μ‚ + 7𝑗 Μ‚ + 3π‘˜ Μ‚ are coplanar.Three vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Given, 𝒂 βƒ— = 𝑖 Μ‚ + 3𝑗 Μ‚ + π‘˜ Μ‚ 𝒃 βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ βˆ’ π‘˜ Μ‚ 𝒄 βƒ— = λ𝑖 Μ‚ + 7𝑗 Μ‚ + 3π‘˜ Μ‚ [π‘Ž βƒ—" " 𝑏 βƒ—" " 𝑐 βƒ— ] = |β– 8(1&3&1@2&βˆ’1&βˆ’1@πœ†&7&3)| 0 = 1[(βˆ’1Γ—3)βˆ’(7Γ—βˆ’1) ] βˆ’ 3[(2Γ—3)βˆ’(Ξ»Γ—βˆ’1) ] + 1[(2Γ—7)βˆ’(Ξ»Γ—βˆ’1) ] 0 = 1 [βˆ’3βˆ’(βˆ’7)]βˆ’3[6βˆ’(βˆ’Ξ»)]+1[14βˆ’(βˆ’Ξ»)] 0 = 1 [βˆ’3+7]βˆ’3[6+Ξ»]+1[14+Ξ»] 0 = 4 – 18 – 3Ξ» + 14 + Ξ» 0 = 18 – 18 – 3Ξ» + Ξ» 0 = – 2Ξ» –2Ξ» = 0 Ξ» = 0/(βˆ’2) 𝝀 = 0 Therefore, π‘Ž βƒ—,𝑏,𝑐 βƒ— are coplanar if Ξ» = 0

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.