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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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.