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If the angles between the vectors a → and b → , b → and c → , c → and a → be π 4 , π 3 , π 3 respectively, then the angle which a → makes with the plane containing b → and c → is

Options

  1. Asin - 1 ⁡ 2 3
  2. Bsin - 1 ⁡ 2 3
  3. Csin - 1 ⁡ 1 4
  4. Dsin - 1 ⁡ 2 3

Correct answer

A. sin - 1 ⁡ 2 3

Step-by-step solution

A normal vector perpendicular to the plane is b → × c → sin ⁡ θ = a → ⋅ b → × c → a → b → × c → = a → b → c → a → b → × c → … i b → × c → = b → c → sin ⁡ π 3 = 3 2 b → c → … i i a → b → c → 2 = a → ⋅ a → a → ⋅ b → a → ⋅ c → b → ⋅ a → b → &

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