This question is the same as Example 27 (Supplementary NCERT)

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.5, 2 (Supplementary NCERT) Show that the vectors ๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚, ๐‘ โƒ— = โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ and ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ 3๐‘— ฬ‚ + 5๐‘˜ ฬ‚ are coplanarThree 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‚ โˆ’ 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ ๐‘ โƒ— = โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ 3๐‘— ฬ‚ + ฮป๐‘˜ ฬ‚ [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(1&โˆ’2&3@โˆ’2&3&โˆ’4@1&โˆ’3&5)| = 1[(3ร—5)โˆ’(โˆ’3ร—โˆ’4) ] โˆ’ (โˆ’2) [(โˆ’2ร—5)โˆ’(1ร—โˆ’4) ] + 3[(โˆ’2ร—โˆ’3)โˆ’(1ร—3) ]

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.