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COMEDK2024MathematicsThree Dimensional Geometry

The angle between the lines x-2 3 = y-1 1 = z+3 -1 and x+1 2 = y-1 -1 = z 2 is

Options

  1. A⁻¹ ( 3 11 )
  2. B⁻¹ ( 3 11 )
  3. C⁻¹ ( 1 11 )
  4. D⁻¹ ( 1 11 )

Correct answer

C. ⁻¹ ( 1 11 )

Step-by-step solution

Let, L₁ x-2 3 = y-1 1 = z+3 -1 Direction ratio of L₁ (l₁, m₁, n₁ )=(3,1,-1) L₂ x+1 2 = y-1 -1 = z-0 2 Direction ratio of L₂ (l₂, m₂, n₂ )=(2,-1,2) aligned & Angle between L₁ and L₂ & = = l₁ L₂+m₁ m₂+n₁ n₂ l₁^2+m₁^2+n₁^2 l₂^2+m₂^2+n₂^2 & = 6-1-2 9+1+1 4+1+4 = 3 3 11 = 1 11 & = ⁻¹ ( 1 11 ) aligned

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