2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Three Dimensional Geometry

JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is [MP PET 1995; RPET 2001]

    A) 12

    B) 50

    C) \[5\sqrt{2}\]

    D) None of these

    Correct Answer: C

    Solution :

    •  Let the line segment be AB, then as given           
    • \[AB\cos \alpha =3\], \[AB\cos \beta =4\,\], \[AB\cos \gamma =5\]           
    • \[\,\Rightarrow \,\,A{{B}^{2}}({{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma )\]\[={{3}^{2}}+{{4}^{2}}+{{5}^{2}}\]           
    • \[AB=\sqrt{9+16+25}=5\sqrt{2}\],                   
    • where \[\alpha ,\,\,\beta \] and \[\gamma \] are the angles made by the line with the axes.


You need to login to perform this action.
You will be redirected in 3 sec spinner