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


Misc 19 If ΞΈ is the angle between any two vectors π‘Ž βƒ— and 𝑏 βƒ—, then |π‘Ž βƒ—" β‹…" 𝑏 βƒ— | = |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | when ΞΈ is equal to (A) 0 (B) πœ‹/4 (C) πœ‹/2 (D) Ο€ π‘Ž βƒ—" β‹…" 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | cos⁑"ΞΈ" |π‘Ž βƒ—" β‹…" 𝑏 βƒ— | = ||π‘Ž βƒ— ||𝑏 βƒ— |cos⁑"ΞΈ" | = |π‘Ž βƒ— ||𝑏 βƒ— | cos⁑"ΞΈ" (π‘Ž ⃗×𝑏 βƒ— ) = |π‘Ž βƒ— ||𝑏 βƒ— | 𝑠𝑖𝑛⁑"ΞΈ" 𝑛 Μ‚ |π‘Ž ⃗×𝑏 βƒ— |= ||π‘Ž βƒ— ||𝑏 βƒ— |sin⁑〖"ΞΈ " 𝑛 Μ‚ γ€— | = |π‘Ž βƒ— ||𝑏 βƒ— |𝑠𝑖𝑛 ΞΈ |𝒏 Μ‚ | = |π‘Ž βƒ— ||𝑏 βƒ— |𝑠𝑖𝑛 ΞΈ Given, |π‘Ž βƒ—" β‹…" 𝑏 βƒ— | = |π‘Ž ⃗×𝑏 βƒ— | So, |π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ = |π‘Ž βƒ— ||𝑏 βƒ— | sin ΞΈ cos ΞΈ = sin ΞΈ We know that cos πœ‹/4 = sin πœ‹/4 = 1/√2 ∴ ΞΈ = 𝝅/πŸ’ Therefore, the angle between the vectors π‘Ž βƒ— and 𝑏 βƒ— is πœ‹/4, So, option (B) is correct.

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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.