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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

Transcript

Misc 17 Let ๐‘Ž โƒ— and ๐‘ โƒ— be two unit vectors and ฮธ is the angle between them. Then ๐‘Ž โƒ— + ๐‘ โƒ— is a unit vector if (A) ฮธ = ๐œ‹/4 (B) ฮธ = ๐œ‹/3 (C) ฮธ = ๐œ‹/2 (D) ฮธ = 2๐œ‹/3 Given ๐‘Ž โƒ— & ๐‘ โƒ— are unit vectors, So, |๐‘Ž โƒ— | = 1 & |๐‘ โƒ— | = 1 We need to find ฮธ if ๐‘Ž โƒ— + ๐‘ โƒ— is a unit vector Assuming ๐‘Ž โƒ— + ๐‘ โƒ— is a unit vector Magnitude of ๐‘Ž โƒ— + ๐‘ โƒ— = 1 |๐‘Ž โƒ—+๐‘ โƒ— |=1 |๐’‚ โƒ—+๐’ƒ โƒ— |^๐Ÿ=1^2 (๐’‚ โƒ—+๐’ƒ โƒ— ).(๐’‚ โƒ—+๐’ƒ โƒ— ) = 1 ๐‘Ž โƒ—. (๐‘Ž โƒ—+๐‘ โƒ— ) + ๐‘ โƒ—. (๐‘Ž โƒ—+๐‘ โƒ— ) = 1 ๐’‚ โƒ— . ๐’‚ โƒ— + ๐‘Ž โƒ— . ๐‘ โƒ— + ๐‘ โƒ—.๐‘Ž โƒ— + ๐’ƒ โƒ—.๐’ƒ โƒ— = 1 |๐’‚ โƒ— |^๐Ÿ + ๐‘Ž โƒ—.๐‘ โƒ— + ๐‘ โƒ—.๐‘Ž โƒ— + |๐’ƒ โƒ— |^๐Ÿ=1 12 + ๐‘Ž โƒ—. ๐‘ โƒ— + ๐‘ โƒ—.๐‘Ž โƒ— + 12 = 1 2 + ๐‘Ž โƒ—. ๐‘ โƒ— + ๐’ƒ โƒ—.๐’‚ โƒ— = 1 2 + ๐‘Ž โƒ—. ๐‘ โƒ— + ๐’‚ โƒ—. ๐’ƒ โƒ— = 1 2 + 2 ๐‘Ž โƒ—. ๐‘ โƒ— = 1 2๐‘Ž โƒ—. ๐‘ โƒ— = 1 โˆ’ 2 ๐‘Ž โƒ—. ๐‘ โƒ— = (โˆ’1)/2 |๐‘Ž โƒ— ||๐‘ โƒ— | cosโก ฮธ = (โˆ’1)/2 1 ร— 1 ร— cos ฮธ = (โˆ’1)/2 cos ฮธ = (โˆ’๐Ÿ)/๐Ÿ We know that cos 60ยฐ = 1/2 & cos is negative in 2nd quadrant, So, ฮธ = 180 โˆ’ 60ยฐ ฮธ = 120ยฐ ฮธ = 120 ร— ๐œ‹/180 ฮธ = 2๐œ‹/3

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.