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
  2. Serial order wise

Transcript

Ex 10.5, 3 (Supplementary NCERT) Find ๐œ† if the vectors ๐‘– ฬ‚ โ€“ ๐‘— ฬ‚ + ๐‘˜ ฬ‚, 3๐‘– ฬ‚ + ๐‘— ฬ‚ + 2๐‘˜ ฬ‚ and ๐‘– ฬ‚ + ๐œ†๐‘— ฬ‚ โ€“ 3๐‘˜ ฬ‚ are coplanar.Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Let ๐’‚ โƒ— = ๐‘– ฬ‚ โ€“ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐’ƒ โƒ— = 3๐‘– ฬ‚ + ๐‘— ฬ‚ + 2๐‘˜ ฬ‚ ๐’„ โƒ— = ๐‘– ฬ‚ + ๐œ†๐‘— ฬ‚ โ€“ 3๐‘˜ ฬ‚ Now, [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(1&โˆ’1&1@3&1&2@1&"๐œ†" &โˆ’3)| 0 = 1[(1ร—โˆ’3)โˆ’("๐œ†" ร—2) ] โˆ’ (โ€“1)[(3ร—โˆ’3)โˆ’(1ร—2) ] + 1[(3ร—"๐œ†" )โˆ’(1ร—1) ] 0 = 1 [โˆ’3โˆ’2"๐œ†" ]+1[โˆ’9โˆ’2]+1[3"๐œ†" โˆ’1] 0 = โ€“3 โ€“ 2๐œ† โ€“ 11 + 3๐œ† โ€“ 1 0 = โ€“3 โ€“ 11 โ€“ 1 + 3๐œ† โ€“ 2ฮป 0 = โ€“15 + ๐œ† 15 = ฮป ๐€ = 15 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ฮป = 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.