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AP EAMCET202420 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The direction cosines of the line of intersection of the planes x+2 y+z-4=0 and 2 x-y+z-3=0 are

Options

  1. A( 3 26 , 1 26 , -4 26 )
  2. B( 3 14 , 2 14 , -1 14 )
  3. C( 3 35 , 1 35 , -5 35 )
  4. D( 3 22 , -2 22 , 3 22 )

Correct answer

C. ( 3 35 , 1 35 , -5 35 )

Step-by-step solution

2 x-y+z-3=0 ... (i) x+2 y+z-4=0 ... (ii) Solving (i) and (ii) x=-1, y=0, z=5 Line of intersection is parallel to r ₁ r ₂ | array ccc i & j & k 2 & -1 & 1 1 & 2 & 1 array |=(3) i - j +5 k Equation of line of intersection of plane. x+1 -3 = y -1 = z-5 5 D.C. are ( -3 35 , -1 35 , 5 35 )

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