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Misc 19 - If |a.b| = |a x b| then theta equal to 0, pi/4

Misc 19 - Chapter 10 Class 12 Vector Algebra - Part 2

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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 eq |𝒂 βƒ—" β‹…" 𝒃 βƒ— | 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" | = |𝒂 βƒ— ||𝒃 βƒ— ||𝒄𝒐𝒔⁑"ΞΈ" | |𝒂 βƒ—" " Γ—" " 𝒃 βƒ— | π‘Ž βƒ— Γ— 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | 𝑠𝑖𝑛⁑"ΞΈ" 𝑛 Μ‚ |π‘Ž βƒ— Γ— 𝑏 βƒ— | = ||π‘Ž βƒ— ||𝑏 βƒ— |⁑〖sin" ΞΈ " 𝑛 Μ‚ γ€— | = |π‘Ž βƒ— ||𝑏 βƒ— ||sin" ΞΈ|" |𝒏 Μ‚ | = |𝒂 βƒ— ||𝒃 βƒ— ||𝐬𝐒𝐧" ΞΈ|" As 𝑛 Μ‚ is unit vector, |𝑛 Μ‚ | = 1 Given, |π‘Ž βƒ—" β‹…" 𝑏 βƒ— | = |π‘Ž ⃗×𝑏 βƒ— | Putting values |π‘Ž βƒ— ||𝑏 βƒ— | |π‘π‘œπ‘ β‘"ΞΈ" | = |π‘Ž βƒ— ||𝑏 βƒ— | |𝑠𝑖𝑛⁑"ΞΈ" | |𝒄𝒐𝒔⁑"ΞΈ" | = |π’”π’Šπ’β‘"ΞΈ" | This is only possible for 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. ual to (A) 0 (B) πœ‹/4 (C) πœ‹/2 (D) Ο€

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.