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MHT CET202120 Sep 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The angle between a line with direction ratios 2, 2, 1 and a line joining (3,1,4) and (7,2,12) is

Options

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

Correct answer

C. ⁻¹ ( 2 3 )

Step-by-step solution

Direction ratios of a line joining (3,1,4) and (7,2,12) are 4,1,8 Let (a₁, b₁, c₁ )=(2,2,1) and (a₂, c₂ )=(4,1,8) . Hence angle between the lines is given by aligned & = a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁ a₂^2+b₂^2+c₂^2 & = 8+2+8 4+4+1 16+1+64 = 18 9 81 = 18 (3)(9) = 2 3 & = ⁻¹ ( 2 3 ) aligned

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