VMMC VMMC Medical Solved Paper-2008

  • question_answer
    The value of P so that the vectors\[2\mathbf{\hat{i}}-\mathbf{\hat{j}}+\mathbf{\hat{k}}\],\[\mathbf{\hat{i}}-2\mathbf{\hat{j}}+3\mathbf{\hat{k}}\]and \[3\mathbf{\hat{i}}-P\mathbf{\hat{j}}+5\mathbf{\hat{k}}\] are coplanar should be

    A)  16         

    B)                                         -4          

    C)         4                                            

    D)         -8

    Correct Answer: B

    Solution :

                    For coplanarity \[\left| \begin{matrix}    2 & -1 & 1  \\    1 & 2 & -3  \\    3 & P & 5  \\ \end{matrix} \right|=0\] \[2(10+3P)+1(5\,+\,9)+1(P-6)=0\] \[20+6P+5+9+P-6=0\]                 \[7P+34-6=0\]                 \[7P+28=0\]                 \[7P=-28\] \[P=-\frac{28}{7}=-4\]


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