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JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

  • question_answer
    If\[a+b+c=0,\left| \overset{\to }{\mathop{a}}\, \right|=3,\left| \overset{\to }{\mathop{b}}\, \right|=5\]and\[\left| \overset{\to }{\mathop{c}}\, \right|=7,\]then the angle between \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\]is then f(1) equals.     JEE Main  Online Paper (Held On 19  May  2012)

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

    B)                        \[\frac{\pi }{4}\]

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

    D)                        \[\frac{\pi }{2}\]

    Correct Answer: A

    Solution :

                    Let\[a+b+c=0\Rightarrow (a+b)=-c\] \[\Rightarrow \]\[{{(a+b)}^{2}}={{c}^{2}}\] \[\Rightarrow \]\[{{a}^{2}}+{{b}^{2}}+2a.b={{c}^{2}}\] \[\Rightarrow \]\[9+25+2.3.5\cos \theta =49\] \[\left( \because \left| \overset{\to }{\mathop{a}}\, \right|=3,\left| \overset{\to }{\mathop{b}}\, \right|=5\,\text{and}\left| \overset{\to }{\mathop{c}}\, \right|=7 \right)\] \[\therefore \]\[\cos \theta =\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}\]


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