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AP EAMCET201921 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual

The angle made by the vector 2 i ¯ - j ¯ + k ¯ with the plane represented by r ¯ · ( i ¯ + j ¯ + 2 k ¯ ) = 7 is

Options

  1. A30 °
  2. B60 °
  3. C45 °
  4. D75 °

Correct answer

A. 30 °

Step-by-step solution

The normal vector is given as n → = i ^ + j ^ + 2 k ^ . The equation of plane is r → · ( i ^ + j ^ + 2 k ^ ) = 7 . The angle made by the vector ( 2 i ^ - j ^ + k ^ ) with i ^ + j ^ + 2 k ^ is cos θ = 2 × 1 + ( - 1 ) × 1 + 1 × 2 2 2 + 1 2 + 1 2 1 2 + 1 2 + 2 2 ⇒ cos θ = 3 6 6 = 1 2 ⇒ θ = 60 ° The angle made by the plane with the vector is 90 ° - 60 ° = 30 ° .

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