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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.5, 4 (Supplementary NCERT) Let ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚, ๐‘ โƒ— = ๐‘– ฬ‚ and ๐‘ โƒ— = c1๐‘– ฬ‚ + c2๐‘— ฬ‚ + c3๐‘˜ ฬ‚ are coplanar (a) If c1 = 1 and c2 = 2, find c3 which makes ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— coplanar Given c1 = 1 and c2 = 2 So, ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = ๐‘– ฬ‚ = ๐‘– ฬ‚ + 0๐‘— ฬ‚ + 0๐‘˜ ฬ‚ ๐‘ โƒ— = c1๐‘– ฬ‚ + c2๐‘— ฬ‚ + c3๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + c3๐‘˜ ฬ‚ Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Finding [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(1&1&1@1&0&0@1&2&๐‘_3 )| 0 = 1[(0ร—๐‘_3 )โˆ’(0ร—2) ] โˆ’ 1[(1ร—๐‘_3 )โˆ’(1ร—0) ] + 1[(1ร—2)โˆ’(1ร—0) ] 0 = 1 [0โˆ’0]โˆ’1[๐‘_3โˆ’0]+1[2โˆ’0] 0 = 0 โ€“ ๐‘_3 + 2 0 = โ€“ ๐‘_3 + 2 ๐’„_๐Ÿ‘ = 2 Therefore, ๐‘Ž โƒ—,๐‘,๐‘ โƒ— are coplanar if ๐‘_3 = 2

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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.