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MHT CET2016MathematicsThree Dimensional Geometry

The acute angle between the line r → = ( i ^ + 2 j ^ + k ^ ) + λ ( i ^ + j ^ + k ^ ) and the plane r → . ( 2 i ^ + j ^ + k ^ ) = 5 is

Options

  1. Acos - 1 ⁡ 2 3
  2. Bsin -1 2 2 3
  3. Ctan - 1 ⁡ 2 3
  4. Dsin - 1 ⁡ 2 3

Correct answer

B. sin -1 2 2 3

Step-by-step solution

The angle between the given line and plane is given by sin θ = | ( i ^ + j ^ + k ^ ) . ( 2 i ^ + j ^ + k ^ ) | i ^ + j ^ + k ^ | | 2 i ^ + j ^ + k ^ | | = 4 3 6 = 2 2 3

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