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AP EAMCET202125 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

If the lengths of projections of a line of length l over the coordinate axes are l₁, l₂ and l₃ respectively, then l₁^2+l₂^2+l₃^2 is equal to

Options

  1. A2 l^2
  2. B3 l^2
  3. Cl^2
  4. D5 l^2

Correct answer

C. l^2

Step-by-step solution

It d be the length of line, then projection on X-axis = dl, projection on Y-axis = dm and projection on Z-axis = dn aligned & Given, d=l and d l=l₁ & array l d m=l₂ and d n=l₃ array aligned aligned & Now, (d l)^2+(d m)^2+(d n)^2=l₁^2+l₂^2+l₃^2 & d^2 (l^2+m^2+n^2 )=l₁^2+l₂^2+l₃^2 l^2+m^2+n^2=1 & l^2 l=l₁^2+l₂^2+l₃^2 l₁^2+l₂^2+l₃^2=l^2 aligned

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