Example 17 - Chapter 10 Class 12 Vector Algebra

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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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo