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AP EAMCET202423 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the direction cosines of two lines are given by l+m+n=0 and m n-2 l m-2 n l=0 , then the acute angle between those lines is

Options

  1. A2 5
  2. B3
  3. C4
  4. D60

Correct answer

B. 3

Step-by-step solution

l+m+n=0 l=-m-n ...(i) aligned & and m n-2 l m-2 n l=0 & m n+2(m+n) m+2(m+n) n=0 & (2 m+n)(m+2 n)=0 n=-2 m or m=-2 n & l=m or l=n aligned Direction ratios of lines are (1,1,-2) and (1,-2,1) , then angle between them is given by = | 1-2-2 6 6 |= 1 2 = 3

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