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

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Misc 16 If θ is the angle between two vectors 𝑎 ⃗ and 𝑏 ⃗ , then 𝑎 ⃗ ⋅𝑏 ⃗ ≥ 0 only when (A) 0 < 𝜃< 𝜋/2 (B) 0 ≤ 𝜃 ≤𝜋/2 (C) 0 < 𝜃 < π (D) 0 ≤𝜃 ≤ 𝜋 Given, 𝑎 ⃗. 𝑏 ⃗ ≥ 0 |𝑎 ⃗ | |𝑏 ⃗ | cos θ ≥ 0 Assuming |𝑎 ⃗ | ≠ 0 and |𝑏 ⃗ | ≠ 0 cos θ ≥ 0/|𝑎 ⃗ ||𝑏 ⃗ | cos θ ≥ 0 ∴ 0 ≤ θ ≤ 𝜋/2 So, (B) is the correct answer

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Davneet Singh

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.