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

Transcript

Supplementary Example 3 Show that the vectors ๐‘Ž โƒ— = โˆ’4๐‘– ฬ‚ โˆ’ 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚, ๐‘ โƒ— = โˆ’๐‘– ฬ‚ + 4๐‘— ฬ‚ + 3๐‘˜ ฬ‚ and ๐‘ โƒ— = โˆ’8๐‘– ฬ‚ โˆ’ ๐‘— 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‘Ž โƒ— = โ€“4๐‘– ฬ‚ โˆ’ 6๐‘— ฬ‚ โ€“ 2๐‘˜ ฬ‚ ๐‘ โƒ— = โˆ’๐‘– ฬ‚ + 4๐‘— ฬ‚ + 3๐‘˜ ฬ‚ ๐‘ โƒ— = โ€“8๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(โˆ’4&โˆ’6&โˆ’2@โˆ’1&4&3@โˆ’8&โˆ’1&3)| = โ€“4[(4ร—3)โˆ’(โˆ’1ร—3) ] โˆ’ (โˆ’6) [(โˆ’1ร—3)โˆ’(โˆ’8ร—3) ] + (โ€“2)[(โˆ’1ร—โˆ’1)โˆ’(โˆ’8ร—4)] = โ€“4 [12+3]+6(โˆ’3+24)โˆ’2[1+32] = โ€“4(15) + 6 (21) โ€“2(33) = โ€“60 + 126 โ€“ 66 = 0 Since [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = 0 Vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar

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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.