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

Transcript

Ex 10.2, 10 Find a vector in the direction of vector 5๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 2๐‘˜ ฬ‚ which has magnitude 8 units.๐‘Ž โƒ— = 5๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 2๐‘˜ ฬ‚ = 5๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ + 2๐‘˜ ฬ‚ Magnitude of ๐‘Ž โƒ— = โˆš(52+(โˆ’1)2+22) |๐‘Ž โƒ— | = โˆš(25+1+4) = โˆš30 Unit vector in direction of ๐‘Ž โƒ— = 1/|๐‘Ž โƒ— | . ๐‘Ž โƒ— ๐‘Ž ฬ‚ = 1/โˆš30 . [5๐‘– ฬ‚โˆ’1๐‘— ฬ‚+2๐‘˜ ฬ‚ ] ๐‘Ž ฬ‚ = 5/โˆš30 ๐‘– ฬ‚ โˆ’ 1/โˆš30 ๐‘— ฬ‚ + 2/โˆš30 ๐‘˜ ฬ‚ Thus, unit vector ๐‘Ž ฬ‚ = 5/โˆš30 ๐‘– ฬ‚ โˆ’ 1/โˆš30 ๐‘— ฬ‚ + 2/โˆš30 ๐‘˜ ฬ‚ Vector with magnitude 1 = 5/โˆš30 ๐‘– ฬ‚ โˆ’ 1/โˆš30 ๐‘— ฬ‚ + 2/โˆš30 ๐‘˜ ฬ‚ Vector with magnitude 8 = 8 [5/โˆš30 ๐‘– ฬ‚" โˆ’ " 1/โˆš30 ๐‘— ฬ‚" + " 2/โˆš30 ๐‘˜ ฬ‚ ] = ๐Ÿ’๐ŸŽ/โˆš๐Ÿ‘๐ŸŽ ๐’Š ฬ‚ โ€“ ๐Ÿ–/โˆš๐Ÿ‘๐ŸŽ ๐’‹ ฬ‚ + ๐Ÿ๐Ÿ”/โˆš๐Ÿ‘๐ŸŽ ๐’Œ ฬ‚ Hence, the required vector is 40/โˆš30 ๐‘– ฬ‚ โ€“ 8/โˆš30 ๐‘— ฬ‚ + 16/โˆš30 ๐‘˜ 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.