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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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’‚ โƒ— = ๐‘– ฬ‚ + 3๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐’ƒ 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.