Misc 4 - If a = b + c, then is it true that |a| = |b| + |c|

Misc 4 - Chapter 10 Class 12 Vector Algebra - Part 2
Misc 4 - Chapter 10 Class 12 Vector Algebra - Part 3

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

Transcript

Misc 4 If ๐‘Ž โƒ— = ๐‘ โƒ— + ๐‘ โƒ— , then is it true that |๐‘Ž โƒ—|=|๐‘ โƒ—| + |๐‘ โƒ—| Justify your answer.Given, ๐’‚ โƒ— = ๐’ƒ โƒ— + ๐’„ โƒ— Let ๐’ƒ โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ & ๐’„ โƒ— = 2๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ Thus, ๐’‚ โƒ— = (๐‘ โƒ— + ๐‘ โƒ—) = (1 + 2) ๐‘– ฬ‚ + (2 โˆ’ 1) ๐‘— ฬ‚ + (3 โˆ’ 2) ๐‘˜ ฬ‚ = 3๐’Š ฬ‚ + 1๐’‹ ฬ‚ + 1๐’Œ ฬ‚ Given, ๐’‚ โƒ— = ๐’ƒ โƒ— + ๐’„ โƒ— Let ๐’ƒ โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ & ๐’„ โƒ— = 2๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ Thus, ๐’‚ โƒ— = (๐‘ โƒ— + ๐‘ โƒ—) = (1 + 2) ๐‘– ฬ‚ + (2 โˆ’ 1) ๐‘— ฬ‚ + (3 โˆ’ 2) ๐‘˜ ฬ‚ = 3๐’Š ฬ‚ + 1๐’‹ ฬ‚ + 1๐’Œ ฬ‚ Given, ๐’‚ โƒ— = ๐’ƒ โƒ— + ๐’„ โƒ— Let ๐’ƒ โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ & ๐’„ โƒ— = 2๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ Thus, ๐’‚ โƒ— = (๐‘ โƒ— + ๐‘ โƒ—) = (1 + 2) ๐‘– ฬ‚ + (2 โˆ’ 1) ๐‘— ฬ‚ + (3 โˆ’ 2) ๐‘˜ ฬ‚ = 3๐’Š ฬ‚ + 1๐’‹ ฬ‚ + 1๐’Œ ฬ‚ Finding |๐’‚ โƒ— |, |๐’ƒ โƒ— | , |๐’„ โƒ— | Magnitude of ๐‘Ž โƒ— = โˆš(32+1^2+1^2 ) |๐’‚ โƒ— | = โˆš(9+1+1) = โˆš๐Ÿ๐Ÿ Magnitude of ๐‘ โƒ— = โˆš(12+22+32) |๐’ƒ โƒ— | = โˆš(1+4+9) = โˆš๐Ÿ๐Ÿ’ Magnitude of ๐‘ โƒ— = โˆš(22+(โˆ’1)2+(โˆ’2)2) |๐’„ โƒ— | = โˆš(4+1+4) = โˆš9 = 3 Now, |๐’ƒ โƒ— | + |๐’„ โƒ— | = โˆš14 + 3 โ‰  โˆš11 โ‰  |๐’‚ โƒ— | So, |๐‘Ž โƒ— |โ‰  |๐‘ โƒ— | + |๐‘ โƒ— | Hence, the given statement is False.

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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.