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

Transcript

Example 28 (Supplementary NCERT) Find ๐œ† if the vectors ๐‘Ž โƒ— = ๐‘– ฬ‚ + 3๐‘— ฬ‚ + ๐‘˜ ฬ‚, ๐‘ โƒ— = 2๐‘– ฬ‚ โ€“ ๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ and ๐‘ โƒ— = ๐œ†๐‘– ฬ‚ + 7๐‘— ฬ‚ + 3๐‘˜ ฬ‚ are coplanar.Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Given, ๐‘Ž โƒ— = ๐‘– ฬ‚ + 3๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = 2๐‘– ฬ‚ โ€“ ๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ ๐‘ โƒ— = ฮป๐‘– ฬ‚ + 7๐‘— ฬ‚ + 3๐‘˜ ฬ‚ [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(1&3&1@2&โˆ’1&โˆ’1@๐œ†&7&3)| 0 = 1[(โˆ’1ร—3)โˆ’(7ร—โˆ’1) ] โˆ’ 3[(2ร—3)โˆ’(ฮปร—โˆ’1) ] + 1[(2ร—7)โˆ’(ฮปร—โˆ’1) ] 0 = 1 [โˆ’3โˆ’(โˆ’7)]โˆ’3[6โˆ’(โˆ’ฮป)]+1[14โˆ’(โˆ’ฮป)] 0 = 1 [โˆ’3+7]โˆ’3[6+ฮป]+1[14+ฮป] 0 = 4 โ€“ 18 โ€“ 3ฮป + 14 + ฮป 0 = 18 โ€“ 18 โ€“ 3ฮป + ฮป 0 = โ€“ 2ฮป โ€“2ฮป = 0 ฮป = 0/(โˆ’2) ๐€ = 0 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ฮป = 0

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.