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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&[email protected]&βˆ’1&βˆ’[email protected]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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.