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

  • question_answer
    If \[\overset{\to }{\mathop{a}}\,=\hat{i}-2\hat{j}+3\hat{k},\overset{\to }{\mathop{b}}\,=2\hat{i}+3\hat{j}-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=r\hat{i}+\hat{j}+\left( 2r-1 \right)\hat{k}\]are three vectors such  that \[\overset{\to }{\mathop{c}}\,\] is parallel to the plane of \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,,\] then r is equal to     JEE Main  Online Paper (Held On 19  May  2012)

    A) 1                                             

    B)                        -1

    C)                        0  

    D)                        2

    Correct Answer: C

    Solution :

                    Let\[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\]and \[\vec{c}=r\hat{i}+\hat{j}+(2r-1)\hat{k}\] Since, \[\vec{c}\]is parallel to the plane of \[\vec{a}\] and \[\vec{b}\] therefore, \[\vec{a},\vec{b}\]and\[\vec{c}\] are coplanar. \[\therefore \]\[\left| \begin{matrix}    1 & -2 & 3  \\    2 & 3 & -1  \\    r & 1 & 2r-1  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1(6r-3+1)+2(4r-2+r)+\]\[3(2-3r)=0\] \[\Rightarrow \]\[6r-2+10r-4+6-9r=0\]\[\Rightarrow \]\[r=0\]                                


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