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JEE Advanced2006MathematicsVector AlgebraActual

Let A be vector parallel to line of intersection of planes P₁ and P₂ through origin. P₁ is parallel to the vectors 2 j +3 k and 4 j -3 k and P₂ is parallel to j - k and 3 i +3 j , then the angle between vector A and 2 i + j -2 k is

Options

  1. A2
  2. B4
  3. C6
  4. D3 4

Correct answer

B. 4

Step-by-step solution

Let vector A O be parallel to line of intersection of planes P₁ and P₂ through, i.e. aligned & [(2 j +3 k ) (4 j -3 k )] [( j - k ) (3 i +3 j )]=54( j - k ) . & Angle between 54( j - k ) and (2 i + j -2 k ) & = ( 54+108 3.54 2 )= 1 2 & = 4 , 3 4 aligned

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