J & K CET Engineering J and K - CET Engineering Solved Paper-2009

  • question_answer A line makes an obtuse angle with the positive x-axis and angles \[\frac{\pi }{4}\] and \[\frac{\pi }{3}\] with the positive y and z axes respectively. Its direction cosine are

    A)  \[\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{2}\]

    B)  \[\frac{1}{\sqrt{2}},-\frac{1}{2},\frac{1}{2}\]

    C)  \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]

    D)  \[\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2}\]

    Correct Answer: C

    Solution :

    Let \[m=\cos \frac{\pi }{4}=\frac{1}{\sqrt{2}}\] and    \[n=\cos \frac{\pi }{3}=\frac{1}{2}\] \[\because \] \[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1\] \[\Rightarrow \]   \[l=\sqrt{1-({{m}^{2}}+{{n}^{2}})}=\sqrt{1-\left( \frac{1}{2}+\frac{1}{4} \right)}\] \[=\sqrt{1-\frac{3}{4}}\] \[\Rightarrow \] \[l=\pm \frac{1}{2}\] Since, line makes an obtuse angle, so we angle \[l=-\frac{1}{2}\] \[\therefore \]   Direction cosines are \[-\frac{1}{2},\frac{1}{\sqrt{2}},\frac{1}{2},\]


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