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AP EAMCET202422 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

If a line L makes angles 3 and 4 with Y -axis and Z -axis respectively, then the angle between L and another line having direction ratios 1,1,1 is

Options

  1. A⁻¹ ( 2 6 )
  2. B⁻¹ ( 2 +1 3 3 )
  3. C⁻¹ ( 2 -1 3 )
  4. D⁻¹ ( 2 +1 6 )

Correct answer

D. ⁻¹ ( 2 +1 6 )

Step-by-step solution

L makes 3 and 4 angle with Y -axis and Z -axis m= 3 = 1 2 and n= 4 = 1 2 and l^2+m^2+n^2=1 l^2+ 1 4 + 1 2 =1 l= 1 2 Now, angle between L and line with direction ratio's 1,1,1 is aligned & = ( 1 1 2 +1 1 2 +1 1 2 1 4 + 1 4 + 1 2 1+1+1 )= 2 +1 6 & = ⁻¹ ( 2 +1 6 ) aligned

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