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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

If the direction cosines of the two lines satisfy the equations l+m+n=0,2 l m+2 l n-m n=0 , then the acute angle between these lines is

Options

  1. A⁻¹ ( 1 3 )
  2. B30^
  3. C⁻¹ ( 2 3 )
  4. D60^

Correct answer

D. 60^

Step-by-step solution

The direction cosines of two lines satisfy the equations aligned & l+m+n=0 m=-(l+n) & and 2 l m+2 l n-m n=0 & 2 l n+m(2 l-n)=0 & 2 -(l+n)(2 l-n)=0 & 2 l n-2 l^2+n l-2 +n^2=0 & -2 l^2+n l+n^2=0 & 2 l^2-n l-n^2=0 & 2 l^2-2 n l+n l-n^2=0 & 2 l(l-n)+n(l-n)=0 & (l-n)(2 l+n)=0 & l=n and l=- n 2 & aligned If l=n and l=- n 2 Substituting in Eq. (i), gathered m=-(n+n) and m=- (- n 2 +n ) m -2 =n and m=- n 2 gathered From Eqs. (iii) and (iv), l 1 = m -2 = n 1 and l 1 = m 1 = n -2 So, l: m: n=1:-2: 1 and l: m: n=1: 1:-2 So, a

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