Ex 10.3, 9 - Find |x| if for a unit vector a,(x - a).(x + a)= 12

Ex 10.3, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Ex 10.3, 9 Find |๐‘ฅ โƒ— |, if for a unit vector ๐‘Ž โƒ—, (๐‘ฅ โƒ— โˆ’ ๐‘Ž โƒ—).(๐‘ฅ โƒ— + ๐‘Ž โƒ—) = 12.Given ๐‘Ž โƒ— is a unit vector So, ๐‘Ž โƒ— has a magnitude 1. โˆด |๐’‚ โƒ— | = 1. Given that (๐‘ฅ โƒ— โˆ’ ๐‘Ž โƒ—) โ‹… (๐‘ฅ โƒ— + ๐‘Ž โƒ—) = 12 ๐‘ฅ โƒ— . ๐‘ฅ โƒ— + ๐‘ฅ โƒ— . ๐‘Ž โƒ— โˆ’ ๐’‚ โƒ— . ๐’™ โƒ— โˆ’ ๐‘Ž โƒ— . ๐‘Ž โƒ— = 12 ๐‘ฅ โƒ— . ๐‘ฅ โƒ— + ๐‘ฅ โƒ— . ๐‘Ž โƒ— โˆ’ ๐’™ โƒ— . ๐’‚ โƒ— โˆ’ ๐‘Ž โƒ— . ๐‘Ž โƒ— = 12 ๐’™ โƒ— . ๐’™ โƒ— โˆ’ ๐’‚ โƒ— . ๐’‚ โƒ— = 12 |๐’™ โƒ— |2 โˆ’ |๐’‚ โƒ— |2 = 12 |๐‘ฅ โƒ— |2 โˆ’ 12 = 12 |๐‘ฅ โƒ— |2 = 12 + 1 (Using prop : ๐‘ฅ โƒ— . ๐‘Ž โƒ— = ๐‘Ž โƒ— . ๐‘ฅ โƒ— ) |๐‘ฅ โƒ— |2 = 13 |๐‘ฅ โƒ— | = ยฑ โˆš13 Since, magnitude of a vector is not negative, โˆด |๐’™ โƒ— | = โˆš๐Ÿ๐Ÿ‘

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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.