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NDA2021MathematicsThree Dimensional GeometryActual

What is the angle between the two lines having direction ratios (6,3,6) and (3,3,0) ?

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

B. 4

Step-by-step solution

Angle between two lines = a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 Here, (a₁, b₁, c₁ )=(6,3,6) and (a₂, b₂, c₂ )=(, 33,0) = 6 3+3 3+0 6^2+3^2+6^2 3^2+3^2+0 aligned & = 27 9 3 2 = 1 2 & = ⁻¹ ( 1 2 )= 4 aligned

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