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

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  1. Chapter 10 Class 12 Vector Algebra
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Misc 19 If θ is the angle between any two vectors 𝑎﷯ and 𝑏﷯, then 𝑎﷯ ⋅ 𝑏﷯﷯ = 𝑎﷯ × 𝑏﷯﷯ when θ is equal to (A) 0 (B) 𝜋﷮4﷯ (C) 𝜋﷮2﷯ (D) π Given, 𝑎﷯ ⋅ 𝑏﷯﷯ = 𝑎﷯× 𝑏﷯﷯ So, 𝑎﷯﷯ 𝑏﷯﷯ cos θ = 𝑎﷯﷯ 𝑏﷯﷯ sin θ cos θ = sin θ We know, that cos 𝜋﷮4﷯ = sin 𝜋﷮4﷯ = 1﷮ ﷮2﷯﷯ ∴ θ = 𝝅﷮𝟒﷯ Therefore, the angle between the vectors 𝑎﷯ and 𝑏﷯ is 𝜋﷮4﷯, So, option (B) is correct.

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