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

Transcript

Supplementary Exercise Q5 Find the value of ๐œ† if the following vectors are co-planar (i) ๐‘Ž โƒ— = 2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚, ๐‘ โƒ— = ๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚, and ๐‘ โƒ— = 3๐‘– ฬ‚ โˆ’ ๐œ†๐‘— ฬ‚ + 5๐‘˜ ฬ‚ Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Given, ๐‘Ž โƒ— = 2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = ๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚ ๐‘ โƒ— = 3๐‘– ฬ‚ โˆ’ ฮป ๐‘— ฬ‚ + 5๐‘˜ ฬ‚ [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(2&โˆ’1&1@1&2&โˆ’3@3&โˆ’๐œ†&5)| 0 = 2[(2ร—5)โˆ’(โˆ’ฮปร—โˆ’3) ] โˆ’ (โˆ’1) [(1ร—5)โˆ’(3ร—โˆ’3) ] + 1[(1ร—โˆ’ฮป)โˆ’(3ร—2) ] 0 = 2[10โˆ’3ฮป] + [5+9 ] + [โˆ’ฮปโˆ’6] 0 = 20 โ€“ 6ฮป + 14 โ€“ ฮป +โ€“ 6 0 = โ€“7ฮป + 28 7ฮป = 28 ฮป = 28/7 ๐€ = 4 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ฮป = 4 Supplementary Exercise Q5 Find the value of ๐œ† if the following vectors are co-planar (ii) ๐‘Ž โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚, ๐‘ โƒ— = 2๐‘– ฬ‚ โˆ’ ๐œ†๐‘— ฬ‚ + ๐‘˜ ฬ‚, and ๐‘ โƒ— = 5๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚ Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Given, ๐‘Ž โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = 2๐‘– ฬ‚ โˆ’ ฮป๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = 5๐‘– ฬ‚ + ๐‘— ฬ‚ โ€“ 3๐‘˜ ฬ‚ [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(2&1&1@2&โˆ’๐œ†&1@5&1&โˆ’3)| 0 = 2[(โˆ’ฮปร—โˆ’3)โˆ’(1ร—1)] โˆ’ 1[(2ร—โˆ’3)โˆ’(5ร—1)] + 1[(2ร—1)โˆ’(5ร—โˆ’ฮป) ] 0 = 2[3ฮปโˆ’1] โˆ’ 1[โˆ’6โˆ’5] + 1[2+5ฮป] 0 = 6ฮป โ€“ 2 + 11 + 2 + 5ฮป 0 = 11ฮป + 11 โ€“11ฮป = 11 ฮป = 11/(โˆ’11) ๐€ = โ€“1 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ฮป = โ€“1

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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.