Misc 16 - If a.b >= 0, then only when (A) 0 < theta < pi/2 - Miscellaneous

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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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 𝑎﷯ . 𝑏﷯ = | 𝑎﷯| | 𝑏﷯| cos θ where θ is the angle between 𝑎﷯ and 𝑏﷯ 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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