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AP EAMCET202420 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The angle between the line with the direction ratios (2,5,1) and the plane 8 x+2 y-z=4 is

Options

  1. A⁻¹ ( 64 9804 )
  2. B⁻¹ ( 64 9804 )
  3. C⁻¹ ( 25 2070 )
  4. D⁻¹ ( 25 2070 )

Correct answer

C. ⁻¹ ( 25 2070 )

Step-by-step solution

Direction ratio of line =[2,5,1] Direction ratio of normal of plane =[8,2,-1] Angle between line and plane aligned & = | a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 | & = 16+10-1 4+25+1 64+4+1 = 25 30 69 = 25 2070 & = ⁻¹ ( 25 2070 ) aligned

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