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AP EAMCET202420 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

If L₁ and L₂ are two lines which pass through origin and having direction ratios (3,1,-5) and (2,3,-1) respectively, then equation of the plane containing L₁ and L₂ is

Options

  1. A4 x+5 y-63=0
  2. B5 x-y+3 z=0
  3. C2 x-y+z=0
  4. Dx-5 y+3 z=0

Correct answer

C. 2 x-y+z=0

Step-by-step solution

Equation of L ₁ will be x 3 = y 1 = z -5 Equation of L ₂ will be x 2 = y 3 = z -1 aligned & r ₁=3 i + j -5 k , r ₂=2 i +3 j - k & n = | array ccc i & j & k 3 & 1 & -5 2 & 3 & -1 array | & =(-1+15) i -(-3+10) j +7 k =14 i -7 j +7 k aligned Equation of plane is aligned & 14(x-0)-7(y-0)+7(z-0)=0 & 2 x-y+z=0 aligned

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