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

Transcript

Supplementary Example 4 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‚ + ๐œ†๐‘˜ ฬ‚ are co-planar if ๐œ† = 5 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‚ 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&๐œ†)| 0 = 1[(3ร—ฮป)โˆ’(โˆ’3ร—โˆ’4) ] โˆ’ (โˆ’2) [(โˆ’2ร—ฮป)โˆ’(1ร—โˆ’4) ] + 3[(2ร—โˆ’3)โˆ’(1ร—3) ] 0 = 1 [3ฮปโˆ’12]+2[โˆ’2ฮปโˆ’(โˆ’4)]+3[6โˆ’3] 0 = 3ฮป โ€“ 12 โ€“ 4ฮป + 8 + 9 0 = โ€“ ฮป + 5 ๐€ = 5 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ฮป = 5

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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.