If a.a = 0 and a.b = 0, then what can be concluded about the vector b?

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

Ex 10.3, 12 - Chapter 10 Class 12 Vector Algebra - Part 3

Ex 10.3, 12 - Chapter 10 Class 12 Vector Algebra - Part 4

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

Transcript

Ex 10.3, 12 (Introduction) If ๐‘Ž โƒ— .๐‘Ž โƒ— = 0 & ๐‘Ž โƒ— . ๐‘ โƒ— = 0, then what can be concluded about the vector ๐‘ โƒ—? ๐‘Ž โƒ— . ๐‘ โƒ— = |๐‘Ž โƒ— | |๐‘ โƒ— | cos ฮธ , ฮธ in the angle b/w ๐‘Ž โƒ— and ๐‘ โƒ— Let ๐‘Ž โƒ— = 0 โƒ— = 0๐‘– ฬ‚ + 0๐‘— ฬ‚ + 0๐‘˜ ฬ‚ ๐’‚ โƒ— = 0๐’Š ฬ‚ + 0๐’‹ ฬ‚ + 0๐’Œ ฬ‚ Let ๐’ƒ โƒ— = 8๐’Š ฬ‚ โ€“ 5๐’‹ ฬ‚ + 2๐’Œ ฬ‚ ๐‘Ž โƒ—. ๐‘ โƒ— = 0.8 + 0.(โ€“5) + 0.2 = 0 + 0 + 0 = 0 So, ๐‘Ž โƒ—. ๐‘ โƒ— = 0 ๐’‚ โƒ— = 0๐’Š ฬ‚ + 0๐’‹ ฬ‚ + 0๐’Œ ฬ‚ Let ๐’ƒ โƒ— = 3๐’Š ฬ‚ โ€“ 4๐’‹ ฬ‚ + 7๐’Œ ฬ‚ ๐‘Ž โƒ—. ๐‘ โƒ— = 0.3 + 0(โˆ’4) + 0.7 = 0 + 0 + 0 = 0 So, ๐‘Ž โƒ—. ๐‘ โƒ— = 0 Hence, if ๐‘Ž โƒ— = 0 โƒ—, then ๐‘Ž โƒ—.๐‘ โƒ— = 0 for any vector ๐‘ โƒ— Ex 10.3, 12 If ๐‘Ž โƒ— .๐‘Ž โƒ— = 0 and ๐‘Ž โƒ— . ๐‘ โƒ— = 0, then what can be concluded about the vector ๐‘ โƒ— ? Given, ๐‘Ž โƒ—. ๐‘Ž โƒ— = 0 |๐‘Ž โƒ— | |๐‘Ž โƒ— | cos 0 = 0 |๐‘Ž โƒ— |2 cos 0 = 0 |๐‘Ž โƒ— |2 ร— 1 = 0 |๐‘Ž โƒ— |2 = 0 |๐‘Ž โƒ— | = 0 So, ๐‘Ž โƒ— = 0 โƒ— Now it is given, ๐‘Ž โƒ— . ๐‘ โƒ— = 0 0 โƒ— . ๐‘ โƒ— = 0 is true, for any vector ๐‘ โƒ— Therefore, if ๐‘Ž โƒ— . ๐‘Ž โƒ— = 0 and ๐‘Ž โƒ— . ๐‘ โƒ— = 0, then ๐‘Ž โƒ— = 0 โƒ— and ๐’ƒ โƒ— can be any vector

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.