Example 8 - Find unit vector in direction of sum of vectors

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Example 8 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Example 8 Find the unit vector in the direction of the sum of the vectors, ๐‘Ž โƒ— = 2๐‘– ฬ‚ + 2 ๐‘— ฬ‚ โ€“ 5๐‘˜ ฬ‚ and ๐‘ โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ Given ๐’‚ โƒ— = 2๐‘– ฬ‚ + 2๐‘— ฬ‚ โ€“ 5๐‘˜ ฬ‚ ๐’ƒ โƒ— = 2๐‘– ฬ‚ + 1๐‘— ฬ‚ + 3๐‘˜ ฬ‚ Let ๐’„ โƒ— = (๐’‚ โƒ— + ๐’ƒ โƒ—) = (2 + 2) ๐‘– ฬ‚ + (2 + 1) ๐‘— ฬ‚ + (โ€“5 + 3) ๐‘˜ ฬ‚ = 4๐‘– ฬ‚ + 3๐‘— ฬ‚ โ€“ 2๐‘˜ ฬ‚ โˆด ๐’„ โƒ— = 4๐’Š ฬ‚ + 3๐’‹ ฬ‚ โ€“ 2๐’Œ ฬ‚ Magnitude of ๐‘ โƒ— = โˆš(42+32+(โˆ’2)2) |๐’„ โƒ— | = โˆš(16+9+4) = โˆš๐Ÿ๐Ÿ— Unit vector in direction of ๐‘ โƒ— = ๐Ÿ/|๐’„ โƒ— | ๐’„ โƒ— ๐‘ ฬ‚ = 1/โˆš29 ["4" ๐‘– ฬ‚" + 3" ๐‘— ฬ‚" โˆ’ 2" ๐‘˜ ฬ‚ ] ๐‘ ฬ‚ = 4/โˆš29 ๐‘– ฬ‚" " + 3/โˆš29 ๐‘— ฬ‚" "โ€“ 2/โˆš29 ๐‘˜ ฬ‚" " Thus, Required unit vector = ๐Ÿ’/โˆš๐Ÿ๐Ÿ— ๐’Š ฬ‚" " + ๐Ÿ‘/โˆš๐Ÿ๐Ÿ— ๐’‹ ฬ‚" "โ€“ 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 10 years. He provides courses for Maths and Science at Teachoo.