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JEE Main201815 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

An angle between the plane, x+y+z=5 and the line of intersection of the planes, 3 x+4 y+z-1=0 and 5 x+8 y+2 z+14=0 , is

Options

  1. A⁻¹ ( 3 17 )
  2. B⁻¹ ( 3 17 )
  3. C⁻¹ ( 3 17 )
  4. D⁻¹ ( 3 17 )

Correct answer

D. ⁻¹ ( 3 17 )

Step-by-step solution

Normal to 3 x+4 y+z=1 is 3 i +4 j +k . Normal to 5 x+8 y+2 z=-14 is 5 i +8 j +2 k The line of intersection of the planes is perpendicular to both normals, so, direction ratios of the intersection line are directly proportional to the cross product of the normal vectors. Therefore the direction ratios of the line is - j +4 k Hence the angle between the plane x+y+z+5=0 and the intersection line is ⁻¹ ( -1+4 17 3 )= ⁻¹ ( 3 17 )

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