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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    The angle between the lines whose direction cosines satisfy the equations\[l+m+n=0,\,\,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\], is given by

    A) \[\frac{2\pi }{3}\]                                            

    B) \[\frac{\pi }{6}\]

    C)  \[\frac{5\pi }{3}\]                                           

    D)  \[\frac{\pi }{3}\]

    Correct Answer: D

    Solution :

    Given,\[l+m+n=0\]                                         ? (i)                 \[{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\]                                           ... (ii) Also\[,\]               \[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1\]                                          ... (iii) On solving Eqs. (i), (ii) and (iii), we get                 \[m=\pm \frac{1}{\sqrt{2}},\,\,n=\mp \frac{1}{\sqrt{2}}\]and\[l=0\] \[\therefore \]  \[\theta =\frac{\pi }{3}\]or\[\frac{\pi }{2}\]


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