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JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    Statement-1: The vectors \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,\]and \[\overset{\to }{\mathop{c}}\,\] lie in the same plane if and only if \[\overset{\to }{\mathop{a}}\,.\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\, \right)=0\] Statement-2: The vectors \[\overset{\to }{\mathop{u}}\,\]and \[\overset{\to }{\mathop{v}}\,\] are perpendicular if and only if \[\overset{\to }{\mathop{u}}\,.\overset{\to }{\mathop{v}}\,=0\]where\[\overset{\to }{\mathop{u}}\,\times \overset{\to }{\mathop{v}}\,\]is a vector perpendicular to the plane of.   JEE Main Online Paper (Held On 26-May-2012)  

    A) Statement 1 is false. Statement 2 is true.

    B) Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.

    C) Statement 1 is true, Statement 2 is false.

    D) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

    Correct Answer: C

    Solution :

    Statement - 1 The vectors \[\vec{a},\vec{b}\] and \[\vec{c}\] lie in the same plane. \[\Rightarrow \]\[\vec{a},\vec{b}\] and \[\vec{c}\] are coplanar. We know, the necessary and sufficient conditions for three vectors to be coplanar is that \[[\vec{a}\vec{b}\vec{c}]=0\]i.e. \[\vec{a}.(\vec{b}\times \vec{c})=0\] Hence, statement-1 is true.


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