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

Transcript

Misc 7 If ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚, ๐‘ โƒ— = 2๐‘– ฬ‚ โˆ’๐‘— ฬ‚ + 3๐‘˜ ฬ‚ and ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚ , find a unit vector parallel to the vector 2๐‘Ž โƒ— โ€“ ๐‘ โƒ— + 3๐‘ โƒ— . Given ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚ Let ๐‘Ÿ โƒ— = 2๐‘Ž โƒ— โˆ’ ๐‘ โƒ— + 3๐‘ โƒ— = 2(๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚) โˆ’ (2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 3๐‘˜ ฬ‚) + 3(๐‘– ฬ‚ โˆ’2๐‘— ฬ‚ + ๐‘˜ ฬ‚) = 2๐‘– ฬ‚ + 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚ โˆ’ 2๐‘– ฬ‚ + 1๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚ + 3๐‘– ฬ‚ โˆ’ 6๐‘— ฬ‚ + 3๐‘˜ ฬ‚ = (2 โˆ’ 2 + 3) ๐‘– ฬ‚ + (2 + 1 โˆ’ 6) ๐‘— ฬ‚ + (2 โˆ’ 3 + 3) ๐‘˜ ฬ‚ = 3๐‘– ฬ‚ โ€“ 3๐‘— ฬ‚ + 2๐‘˜ ฬ‚ โˆด ๐’“ โƒ— = 3๐’Š ฬ‚ โ€“ 3๐’‹ ฬ‚ + 2๐’Œ ฬ‚ Magnitude of ๐‘Ÿ โƒ— = โˆš(32+(โˆ’3)2+22) |๐‘Ÿ โƒ— | = โˆš(9+9+4) = โˆš22 Unit vector in the direction of ๐‘Ÿ โƒ— = 1/|๐‘Ÿ โƒ— | x ๐‘Ÿ โƒ— = 1/โˆš22 ร— [3๐‘– ฬ‚ โˆ’3๐‘— ฬ‚+2๐‘˜ ฬ‚ ] = 3/โˆš22 ๐‘– ฬ‚ โ€“ 3/โˆš22 ๐‘— ฬ‚ + 2/โˆš22 ๐‘˜ ฬ‚ Hence the required vector is ๐Ÿ‘/โˆš๐Ÿ๐Ÿ ๐’Š ฬ‚ โ€“ ๐Ÿ‘/โˆš๐Ÿ๐Ÿ ๐’‹ ฬ‚ + ๐Ÿ/โˆš๐Ÿ๐Ÿ ๐’Œ ฬ‚

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.