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JEE Main202226 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

A vector a → is parallel to the line of intersection of the plane determined by the vectors i ^ , i ^ + j ^ and the plane determined by the vectors i ^ - j ^ , i ^ + k ^ . The obtuse angle between a → and the vector b → = i ^ - 2 j ^ + 2 k ^ is

Options

  1. A3 π 4
  2. B2 π 3
  3. C4 π 5
  4. D5 π 6

Correct answer

A. 3 π 4

Step-by-step solution

The normal to the plane determined by the vectors i ^ ,   i ^ + j ^ will be n → 1 = i ^ × i ^ + j ^ = k ^ The normal to the plane determined by the vectors i ^ - j ^ ,   i ^ + k ^ will be n → 2 = i ^ + k ^ × i ^ - j ^ = i ^ + j ^ - k ^ Now the vector along the line of intersection will be n → 1 × n → 2 = k ^ × i ^ + j ^ - k ^ = - i ^ + j ^ i.e. a → = - i ^ + j ^ Given b → = i ^ - 2 j ^ + 2 k ^ a → · b → = - 3 Let a → ∧ b

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