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

Transcript

Misc 1 Write down a unit vector in XY-plane, making an angle of 30ยฐ with the positive direction of x-axis.Let the unit vector be ๐‘Ž โƒ— We know that ๐‘Ž โƒ— = ๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ + z๐‘˜ ฬ‚ Since the vector is in X-Y plane, there is no zโ€“ coordinate. Hence, ๐‘Ž โƒ— = x๐‘– ฬ‚ + y๐‘— ฬ‚ + 0๐’Œ ฬ‚ ๐’‚ โƒ— = ๐’™๐’Š ฬ‚ + y๐’‹ ฬ‚ Unit vector in direction of x axis is ๐‘– ฬ‚ & in y axis is ๐‘— ฬ‚ Given that ๐‘Ž โƒ— makes an angle of 30ยฐ with x-axis So, angle between ๐‘Ž โƒ— & ๐‘– ฬ‚ is 30ยฐ Now, we know that, ๐‘Ž โƒ— . ๐‘ โƒ— = |๐‘Ž โƒ— ||๐‘ โƒ— | cos ฮธ, Putting ๐‘Ž โƒ— = ๐‘Ž โƒ— , ๐‘ โƒ— = ๐‘– ฬ‚ & ฮธ = 30ยฐ ๐’‚ โƒ— .๐’Š ฬ‚ = |๐’‚ โƒ— ||๐’Š ฬ‚ | cos 30ยฐ ๐‘Ž โƒ— .๐‘– ฬ‚ = 1 ร— 1 ร— โˆš3/2 ๐‘Ž โƒ— .๐‘– ฬ‚ = โˆš3/2 (As ๐‘Ž โƒ— is unit vector, |๐‘Ž โƒ— | = 1 & ๐‘– ฬ‚ is a unit vector, |๐‘– ฬ‚ | = 1) (๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ + 0๐‘˜ ฬ‚). ๐‘– ฬ‚ = โˆš3/2 (๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ + 0๐‘˜ ฬ‚). (1๐‘– ฬ‚ + 0๐‘— ฬ‚ + 0๐‘˜ ฬ‚) = โˆš3/2 ๐‘ฅ.1 + y.0 + 0.0 = โˆš3/2 ๐’™=โˆš๐Ÿ‘/๐Ÿ Similarly, ๐‘Ž โƒ— makes an angle of 60ยฐ with y-axis So, angle between ๐’‚ โƒ— & ๐’‹ ฬ‚ is 60ยฐ Now, we know that, ๐‘Ž โƒ— . ๐‘ โƒ— = |๐‘Ž โƒ— ||๐‘ โƒ— | cos ฮธ, Putting ๐‘Ž โƒ— = ๐‘Ž โƒ— , ๐‘ โƒ— = ๐‘— ฬ‚ & ฮธ = 60ยฐ ๐’‚ โƒ— .๐’‹ ฬ‚ = |๐’‚ โƒ— ||๐’‹ ฬ‚ | cos 60ยฐ ๐‘Ž โƒ— .๐‘— ฬ‚ = 1 ร— 1 ร— 1/2 ๐‘Ž โƒ— .๐‘— ฬ‚ = 1/2 (๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ + 0๐‘˜ ฬ‚). ๐‘— ฬ‚ = 1/2 (๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ + 0๐‘˜ ฬ‚). (0๐‘– ฬ‚ + 1๐‘— ฬ‚ + 0๐‘˜ ฬ‚) = 1/2 ๐‘ฅ.0 + y.1 + 0.0 = 1/2 y = ๐Ÿ/๐Ÿ Thus, ๐‘Ž โƒ— = ๐‘ฅ๐‘– ฬ‚ + y๐‘— ฬ‚ = โˆš๐Ÿ‘/๐Ÿ ๐’Š ฬ‚ + ๐Ÿ/๐Ÿ ๐’‹ ฬ‚

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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.