JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer The angle between the two lines\[\frac{x+1}{2}=\frac{y+3}{2}=\frac{z-4}{-1}\]&\[\frac{x-4}{1}=\frac{y+4}{2}=\frac{z+1}{2}\]is

    A) \[{{\cos }^{-1}}\left( \frac{4}{9} \right)\]                               

    B) \[{{\cos }^{-1}}\left( \frac{3}{9} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{2}{9} \right)\]                               

    D) \[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]

    Correct Answer: A

    Solution :

    \[{{a}_{1}}=2,\,\,\,{{b}_{1}}=2,\,\,{{c}_{1}}=-1\]and\[{{a}_{2}}=1,\,\,\,{{b}_{2}}=2,\,\,\,{{c}_{2}}=2\] \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{{{a}_{1}}^{2}+{{b}_{1}}^{2}+{{c}_{1}}^{2}}\sqrt{{{a}_{2}}^{2}+{{b}_{2}}^{2}+{{c}_{2}}^{2}}}\]          \[=\frac{2+4-2}{\sqrt{4+4+1}\sqrt{1+4+4}}=\pm \frac{4}{9}\]

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