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NDA2012MathematicsThree Dimensional GeometryActual

What is the angle between the lines x-2 1 = y+1 -2 = z+2 1 and x-1 1 = 2 y+3 3 = z+5 2 ?

Options

  1. A2
  2. B3
  3. C6
  4. DNone of the above

Correct answer

A. 2

Step-by-step solution

x-2 1 = y+1 -2 = z+2 1 Direction ratios are proportional to 1,-2,1 x-1 1 = y+ 3 2 3 2 = z+5 2 = a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 = (1)(1)+(-2) ( 3 2 )+(1)(2) 1^2+(-2)^2-1^2 1^2+ ( 3 2 )^2+(2)^2 = 2 .

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