Ex 10.5, 3 (Supplementary NCERT) - Find lambda if vectors i - j + k

Ex 10.5, 3 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Ex 10.5, 3 (Supplementary NCERT) Find πœ† if the vectors 𝑖 Μ‚ – 𝑗 Μ‚ + π‘˜ Μ‚, 3𝑖 Μ‚ + 𝑗 Μ‚ + 2π‘˜ Μ‚ and 𝑖 Μ‚ + πœ†π‘— Μ‚ – 3π‘˜ Μ‚ are coplanar.Three vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Let 𝒂 βƒ— = 𝑖 Μ‚ – 𝑗 Μ‚ + π‘˜ Μ‚ 𝒃 βƒ— = 3𝑖 Μ‚ + 𝑗 Μ‚ + 2π‘˜ Μ‚ 𝒄 βƒ— = 𝑖 Μ‚ + πœ†π‘— Μ‚ – 3π‘˜ Μ‚ Now, [π‘Ž βƒ—" " 𝑏 βƒ—" " 𝑐 βƒ— ] = |β– 8(1&βˆ’1&1@3&1&2@1&"πœ†" &βˆ’3)| 0 = 1[(1Γ—βˆ’3)βˆ’("πœ†" Γ—2) ] βˆ’ (–1)[(3Γ—βˆ’3)βˆ’(1Γ—2) ] + 1[(3Γ—"πœ†" )βˆ’(1Γ—1) ] 0 = 1 [βˆ’3βˆ’2"πœ†" ]+1[βˆ’9βˆ’2]+1[3"πœ†" βˆ’1] 0 = –3 – 2πœ† – 11 + 3πœ† – 1 0 = –3 – 11 – 1 + 3πœ† – 2Ξ» 0 = –15 + πœ† 15 = Ξ» 𝝀 = 15 Therefore, π‘Ž βƒ—,𝑏,𝑐 βƒ— are coplanar if Ξ» = 15

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.