Example 17 - Chapter 10 Class 12 Vector Algebra

Last updated at July 31, 2026 by

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

Example 17 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 17 Find |š‘Ž āƒ— āˆ’ š‘ āƒ—| , if two vectors a and b are such that |š‘Ž āƒ—| = 2, |š‘ āƒ—| = 3 and š‘Ž āƒ— ā‹… š‘ āƒ— = 4. Given, |š’‚ āƒ— | = 2 , |š’ƒ āƒ— | = 2 & š’‚ āƒ—. š’ƒ āƒ— = 4 We need to find |š‘Ž āƒ—āˆ’š‘ āƒ— | Taking square, |š’‚ āƒ—āˆ’š’ƒ āƒ— |2 = (š’‚ āƒ—āˆ’š’ƒ āƒ—). (š’‚ āƒ—āˆ’š’ƒ āƒ—) = š‘Ž āƒ— . š‘Ž āƒ— āˆ’ š‘Ž āƒ— . š‘ āƒ— āˆ’ š’ƒ āƒ—. š’‚ āƒ— + š‘ āƒ— . š‘ āƒ— = š‘Ž āƒ— . š‘Ž āƒ— āˆ’ š‘Ž āƒ— . š‘ āƒ— āˆ’ š’‚ āƒ— . š’ƒ āƒ— + š‘ āƒ— . š‘ āƒ— = š’‚ āƒ—. š’‚ āƒ— āˆ’ 2š‘Ž āƒ— . š‘ āƒ— + š’ƒ āƒ—. š’ƒ āƒ— = |š’‚ āƒ— |2 āˆ’ 2š‘Ž āƒ—. š‘ āƒ— + |š’ƒ āƒ— |2 = 22 ā€“ 2 Ɨ 4 + 32 = 4 āˆ’ 8 + 9 = 5 Thus, |š’‚ āƒ—āˆ’š’ƒ āƒ— |2 = 5 |š‘Ž āƒ—āˆ’š‘ āƒ— | = Ā± āˆš5 Since magnitude is not negative, So, |š’‚ āƒ—āˆ’š’ƒ āƒ— | = āˆššŸ“

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