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

Transcript

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, our vectors become ๐’‚ โƒ— = ๐’Š ฬ‚ + ๐’‹ ฬ‚ + ๐’Œ ฬ‚ ๐’ƒ โƒ— = ๐‘– ฬ‚ ๐’„ โƒ— = c1๐‘– ฬ‚ + c2๐‘— ฬ‚ + c3๐‘˜ ฬ‚ Three vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 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 (b) If c2 = โ€“1 and c3 = 1, show that no value of c1 can make ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— coplanar Given c2 = โ€“1 and c3 = 1 So, our vectors ๐’‚ โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐’ƒ โƒ— = ๐‘– ฬ‚ ๐’„ โƒ— = c1๐‘– ฬ‚ + c2๐‘— 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@๐‘_1&โˆ’1&1)| = 1[(0ร—1)โˆ’(0ร—โˆ’1) ] โˆ’ 1[(1ร—1)โˆ’(๐‘_1ร—0) ] + 1[(1ร—โˆ’1)โˆ’(๐‘_1ร—0) ] = 1 [0โˆ’0]โˆ’1[1โˆ’0]+1[โˆ’1โˆ’0] = 0 โ€“ 1 โ€“ 1 = โ€“2 Thus, [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] โ‰  0 for any value of c1 So, we can write that ๐‘Ž โƒ—,๐‘ โƒ—,๐‘ โƒ— are not coplanar for any value of c1

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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.