Ex 10.3, 6 - Chapter 10 Class 12 Vector Algebra

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Ex 10.3, 6 - Find |a|, |b|, if (a + b).(a - b) = 8, |a| = 8|b|

Ex 10.3, 6 - Chapter 10 Class 12 Vector Algebra - Part 2

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Transcript

Ex 10.3, 6 Find |๐‘Ž โƒ— | and |๐‘ โƒ— |, if (๐‘Ž โƒ— + b โƒ—) .(๐‘Ž โƒ— โ€“ ๐‘ โƒ—) = 8 and |๐‘Ž โƒ— | = 8 |๐‘ โƒ— | (๐‘Ž โƒ— + b โƒ—) . (๐‘Ž โƒ— โ€“ ๐‘ โƒ—) = 8 ๐‘Ž โƒ—.(๐‘Ž โƒ— โ€“ b โƒ—) + ๐‘ โƒ—.(๐‘Ž โƒ— โˆ’ ๐‘ โƒ—) = 8 ๐‘Ž โƒ—.๐‘Ž โƒ— โˆ’ ๐‘Ž โƒ—.๐‘ โƒ— + ๐’ƒ โƒ—.๐’‚ โƒ— โˆ’ ๐‘ โƒ—.๐‘ โƒ— = 8 ๐‘Ž โƒ—.๐‘Ž โƒ— โˆ’ ๐‘Ž โƒ—.๐‘ โƒ— + ๐’‚ โƒ—.๐’ƒ โƒ— โˆ’ ๐‘ โƒ—.๐‘ โƒ— = 8 ๐’‚ โƒ—.๐’‚ โƒ— โˆ’ ๐’ƒ โƒ—.๐’ƒ โƒ— = 8 |๐’‚ โƒ— |2 โ€“ |๐’ƒ โƒ— |2 = 8 Also given that , |๐‘Ž โƒ— | = 8 |๐‘ โƒ— | Putting this in (1), |๐’‚ โƒ— |2 โ€“ |๐‘ โƒ— |2 = 8 (Using prop: ๐‘Ž โƒ—.๐‘ โƒ— = ๐‘ โƒ—.๐‘Ž โƒ—) (8|๐’ƒ โƒ— |)2 โˆ’ |๐‘ โƒ— |2 = 8 64|๐‘ โƒ— |2 โˆ’ |๐‘ โƒ— |2 = 8 63|๐‘ โƒ— |2 = 8 |๐‘ โƒ— |2 = 8/63 |๐‘ โƒ— | = โˆš8/โˆš63 โˆด |๐’ƒ โƒ— | = (๐Ÿ โˆš๐Ÿ)/(๐Ÿ‘โˆš๐Ÿ•) Also, |๐‘Ž โƒ— | = 8 ร— |๐‘ โƒ— | |๐‘Ž โƒ— | = 8 ร— (2 โˆš2)/(3โˆš7) โˆด|๐’‚ โƒ— | = (๐Ÿ๐Ÿ” โˆš๐Ÿ)/(๐Ÿ‘โˆš๐Ÿ•)

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