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Example 17 - Find |a - b|, if |a| = 2|b| = 3 and a.b = 4 - Examples

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 17 Find |๐‘Žย โƒ— โˆ’ ๐‘ย โƒ—| , if two vectors a and b are such that |๐‘Žย โƒ—| = 2, |๐‘ย โƒ—| = 3 and ๐‘Žย โƒ— โ‹… ๐‘ย โƒ— = 4. Given, |๐‘Žย โƒ— | = 2 , |๐‘ย โƒ— | = 2 & ๐‘Žย โƒ—. ๐‘ย โƒ— = 4 We need to find : |๐‘Žย โƒ—โˆ’๐‘ย โƒ— | Taking square, |๐’‚ย โƒ—โˆ’๐’ƒย โƒ— |2 = (๐’‚ย โƒ—โˆ’๐’ƒย โƒ—). (๐’‚ย โƒ—โˆ’๐’ƒย โƒ—) = ๐‘Žย โƒ— . ๐‘Žย โƒ— โˆ’ ๐‘Žย โƒ— . ๐‘ย โƒ— โˆ’ ๐’ƒย โƒ—. ๐’‚ย โƒ— + ๐‘ย โƒ— . ๐‘ย โƒ— = ๐‘Žย โƒ— . ๐‘Žย โƒ— โˆ’ ๐‘Žย โƒ— . ๐‘ย โƒ— โˆ’ ๐’‚ย โƒ— . ๐’ƒย โƒ— + ๐‘ย โƒ— . ๐‘ย โƒ— = ๐’‚ย โƒ—. ๐’‚ย โƒ— โˆ’ 2๐‘Žย โƒ— . ๐‘ย โƒ— + ๐’ƒย โƒ—. ๐’ƒย โƒ— = |๐’‚ย โƒ— |2 โˆ’ 2๐‘Žย โƒ—. ๐‘ย โƒ— + |๐’ƒย โƒ— |2 = 22 โ€“ 2 ร— 4 + 32 = 4 โˆ’ 8 + 9 = 5 So, |๐‘Žย โƒ—โˆ’๐‘ย โƒ— |2 = 5 |๐‘Žย โƒ—โˆ’๐‘ย โƒ— | = ยฑ โˆš5 Since magnitude is not negative, So, |๐’‚ย โƒ—โˆ’๐’ƒย โƒ— | = โˆš๐Ÿ“

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