Ex 10.2, 9 - For a = 2i - j + 2k, and b = -i + j - k, find unit vector

Ex 10.2, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Ex 10.2, 9 For given vectors, ๐‘Ž โƒ— = 2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 2๐‘˜ ฬ‚ and ๐‘ โƒ— = โˆ’๐‘– ฬ‚ + ๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ , find the unit vector in the direction of the vector ๐‘Ž โƒ— + ๐‘ โƒ—๐‘Ž โƒ— = 2๐‘– ฬ‚ โˆ’ j ฬ‚ + 2๐‘˜ ฬ‚ = 2๐‘– ฬ‚ โ€“ 1๐‘— ฬ‚ + 2๐‘˜ ฬ‚ ๐‘ โƒ— = โˆ’๐‘– ฬ‚ + ๐‘— ฬ‚ โ€“ ๐‘˜ ฬ‚ = โˆ’1๐‘– ฬ‚ + 1๐‘— ฬ‚ โ€“ 1๐‘˜ ฬ‚ Now, (๐‘Ž โƒ— + ๐‘ โƒ—) = (2 โ€“ 1) ๐‘– ฬ‚ + (-1 + 1) ๐‘— ฬ‚ + (2 โ€“ 1) ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 0๐‘— ฬ‚ + 1๐‘˜ ฬ‚ Let ๐‘ โƒ— = ๐‘Ž โƒ— + ๐‘ โƒ— โˆด c โƒ— = 1๐‘– ฬ‚ + 0๐‘— ฬ‚ + 1๐‘˜ ฬ‚ Magnitude of ๐‘ โƒ— = โˆš(12+02+12) |๐‘ โƒ— | = โˆš(1+0+1) = โˆš2 Unit vector in direction of ๐‘ โƒ— = 1/|๐‘ โƒ— | . ๐‘ โƒ— ๐‘ ฬ‚ = 1/โˆš2 [1๐‘– ฬ‚+0๐‘— ฬ‚+1๐‘˜ ฬ‚ ] ๐‘ ฬ‚ = 1/โˆš2 ๐‘– ฬ‚ + 0๐‘— ฬ‚ + 1/โˆš2 ๐‘˜ ฬ‚ ๐‘ ฬ‚ = ๐Ÿ/โˆš๐Ÿ ๐’Š ฬ‚ + ๐Ÿ/โˆš๐Ÿ ๐’Œ ฬ‚ Thus, unit vector in direction of ๐‘ โƒ— = 1/โˆš2 ๐‘– ฬ‚ + 1/โˆš2 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 10 years. He provides courses for Maths and Science at Teachoo.