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 π‘Ž βƒ— .π‘Ž βƒ— = 0 & π‘Ž βƒ— . 𝑏 βƒ— = 0, then what can be concluded about the vector 𝑏 βƒ—? π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— | |𝑏 βƒ— | cos ΞΈ , ΞΈ in the angle b/w π‘Ž βƒ— and 𝑏 βƒ— Let π‘Ž βƒ— = 0 βƒ— = 0𝑖 Μ‚ + 0𝑗 Μ‚ + 0π‘˜ Μ‚ 𝒂 βƒ— = 0π’Š Μ‚ + 0𝒋 Μ‚ + 0π’Œ Μ‚ Let 𝒃 βƒ— = 8π’Š Μ‚ – 5𝒋 Μ‚ + 2π’Œ Μ‚ π‘Ž βƒ—. 𝑏 βƒ— = 0.8 + 0.(–5) + 0.2 = 0 + 0 + 0 = 0 So, π‘Ž βƒ—. 𝑏 βƒ— = 0 𝒂 βƒ— = 0π’Š Μ‚ + 0𝒋 Μ‚ + 0π’Œ Μ‚ Let 𝒃 βƒ— = 3π’Š Μ‚ – 4𝒋 Μ‚ + 7π’Œ Μ‚ π‘Ž βƒ—. 𝑏 βƒ— = 0.3 + 0(βˆ’4) + 0.7 = 0 + 0 + 0 = 0 So, π‘Ž βƒ—. 𝑏 βƒ— = 0 Hence, if π‘Ž βƒ— = 0 βƒ—, then π‘Ž βƒ—.𝑏 βƒ— = 0 for any vector 𝑏 βƒ— Ex 10.3, 12 If π‘Ž βƒ— .π‘Ž βƒ— = 0 and π‘Ž βƒ— . 𝑏 βƒ— = 0, then what can be concluded about the vector 𝑏 βƒ— ? Given, π‘Ž βƒ—. π‘Ž βƒ— = 0 |π‘Ž βƒ— | |π‘Ž βƒ— | cos 0 = 0 |π‘Ž βƒ— |2 cos 0 = 0 |π‘Ž βƒ— |2 Γ— 1 = 0 |π‘Ž βƒ— |2 = 0 |π‘Ž βƒ— | = 0 So, π‘Ž βƒ— = 0 βƒ— Now it is given, π‘Ž βƒ— . 𝑏 βƒ— = 0 0 βƒ— . 𝑏 βƒ— = 0 is true, for any vector 𝑏 βƒ— Therefore, if π‘Ž βƒ— . π‘Ž βƒ— = 0 and π‘Ž βƒ— . 𝑏 βƒ— = 0, then π‘Ž βƒ— = 0 βƒ— and 𝒃 βƒ— 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.