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JEE Main & Advanced AIEEE Paper (Held On 11 May 2011)

  • question_answer
    If the vector \[p\,\hat{i}+\hat{j}+\hat{k},\hat{i}+q\,\hat{j}+\hat{k}\]and \[\,\hat{i}+\hat{j}+r\,\hat{k}\]\[(p\ne q\ne r\ne 1)\] are coplanar, then the value of pqr - (p+q+r) is-     AIEEE  Solved  Paper (Held On 11 May  2011)

    A)  2                 

    B)  0

    C)  -1

    D)  -2

    Correct Answer: D

    Solution :

                    \[\left| \begin{matrix}    p & 1 & 1  \\    1 & q & 1  \\    1 & 1 & r  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[p(qr-1)+1(1-r)+1(1-q)=0\] \[\Rightarrow \]\[pqr-p+1-r+1-q=0\] \[\Rightarrow \]\[pqr-(p+q+r)=-2\]


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