Example 5 - Let a = i + 2j, b = 2i + j. Is |a| = |b|? - Examples

Example 5 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Example 5 Let ๐‘Ž โƒ— = ๐‘– ฬ‚ + 2๐‘— ฬ‚ and ๐‘ โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ . Is |๐‘Ž โƒ— | = |๐‘ โƒ— | ? Are the vectors ๐‘Ž โƒ— and ๐‘ โƒ— equal? Given ๐’‚ โƒ— = ๐‘– ฬ‚ + 2๐‘— ฬ‚ & ๐’ƒ โƒ— = 2๐‘– ฬ‚ + ๐‘— ฬ‚ So, we can we can write, ๐’‚ โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 0๐‘˜ ฬ‚ & ๐’ƒ โƒ— = 2๐‘– ฬ‚ + 1๐‘— ฬ‚ + 0๐‘˜ ฬ‚ Magnitude of ๐’‚ โƒ— |๐‘Ž โƒ— | = โˆš(12+22+02) = โˆš5 Magnitude of ๐’ƒ โƒ— |๐‘ โƒ— | = โˆš(22+12+02) = โˆš5 Therefore, |๐’‚ โƒ— | = |๐’ƒ โƒ— | Checking if ๐’‚ โƒ— and ๐’ƒ โƒ— are equal ๐‘Ž โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 0๐‘˜ ฬ‚ & ๐‘ โƒ— = 2๐‘– ฬ‚ + 1๐‘— ฬ‚ + 0๐‘˜ ฬ‚ Comparing corresponding components, As 1 โ‰  2 Thus, ๐‘Ž โƒ— and ๐‘ โƒ— are not equal since their corresponding components are distinct.

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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.