Example 18 - Chapter 10 Class 12 Vector Algebra

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Example 18 - lf a is a unit vector (x - a) . (x + a) = 8, find x

Example 18 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 18 If š‘Ž āƒ— is a unit vector and (š‘„ āƒ— āˆ’ š‘Ž āƒ—) ā‹… (š‘„ āƒ— + š‘Ž āƒ—) = 8 , then find |š‘„ āƒ—| Given š‘Ž āƒ— is a unit vector So, š‘Ž āƒ— has a magnitude 1. āˆ“ |š’‚ āƒ— | = 1. Given that (š’™ āƒ— āˆ’ š’‚ āƒ—) ā‹… (š’™ āƒ— + š’‚ āƒ—) = 8 š‘„ āƒ— . š‘„ āƒ— + š‘„ āƒ— . š‘Ž āƒ— āˆ’ š’‚ āƒ— . š’™ āƒ— āˆ’ š‘Ž āƒ— . š‘Ž āƒ— = 8 š‘„ āƒ— . š‘„ āƒ— + š‘„ āƒ— . š‘Ž āƒ— āˆ’ š’™ āƒ— . š’‚ āƒ— āˆ’ š‘Ž āƒ— . š‘Ž āƒ— = 8 š’™ āƒ— . š’™ āƒ— āˆ’ š’‚ āƒ— . š’‚ āƒ— = 8 |š’™ āƒ— |2 āˆ’ |š’‚ āƒ— |2 = 8 |š‘„ āƒ— |2 āˆ’ 12 = 8 (Using: š‘„ āƒ— . š‘Ž āƒ— = š‘Ž āƒ— . š‘„ āƒ— ) |š‘„ āƒ— |2 = 8 + 1 |š‘„ āƒ— |2 = 9 |š‘„ āƒ— | = Ā± āˆš9 |š‘„ āƒ— | = Ā± 3 Since magnitude is not negative, āˆ“ |š’™ āƒ— | = 3

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