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JEE Main & Advanced AIEEE Solved Paper-2007

  • question_answer
    Let \[(CIC{{H}_{2}}COOH)\]and\[KMn{{O}_{4}}\] If the vector \[\vec{c}\] lies in the plane of \[\vec{a}\] and \[\vec{b}\], then\[O_{2}^{2-}\]equals

    A)  0                            

    B)         1                            

    C)         -4                          

    D)         -2

    Correct Answer: D

    Solution :

    \[\because \]\[a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}+\hat{j}+2\hat{k}\] and\[c=x\hat{i}+(x-2)\hat{j}-\hat{k}\]are coplanar. \[\therefore \] \[\left| \begin{matrix}    x & x-2 & -1  \\    1 & 1 & 1  \\    1 & -1 & 2  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1\{1-2(x-2)\}-1(-1-2x)+1(x-2+x)=0\] \[\Rightarrow \] \[1-2x+4+1+2x+2x-2=0\] \[\Rightarrow \] \[3x+2-x+2=0\] \[\Rightarrow \] \[2x=-4\] \[\Rightarrow \] \[x=-2\]


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