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Misc 16 - If ΞΈ is angle between two vectors a and b, then a.b >= 0

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Misc 16 If ΞΈ is the angle between two vectors π‘Ž βƒ— and 𝑏 βƒ— , then π‘Ž βƒ— ⋅𝑏 βƒ— β‰₯ 0 only when (A) 0 < πœƒ< πœ‹/2 (B) 0 ≀ πœƒ β‰€πœ‹/2 (C) 0 < πœƒ < Ο€ (D) 0 β‰€πœƒ ≀ πœ‹ Given, π‘Ž βƒ—. 𝑏 βƒ— β‰₯ 0 |π‘Ž βƒ— | |𝑏 βƒ— | cos ΞΈ β‰₯ 0 Assuming |π‘Ž βƒ— | β‰  0 and |𝑏 βƒ— | β‰  0 cos ΞΈ β‰₯ 0/|π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ β‰₯ 0 ∴ 0 ≀ ΞΈ ≀ πœ‹/2 So, (B) is the correct answer

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.