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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    If the points\[(k,3),(2,k),(-k,3)\]are collinear, then the values of k are:

    A)  2, 3                                       

    B)  1, 0

    C)  1, 2                       

    D)         \[1,-1/2\]

    E)  0, 3

    Correct Answer: E

    Solution :

    \[\because \]Points\[(k,3),(2,k),(-k,3)\]are collinear. \[\left| \begin{matrix}    k & 3 & 1  \\    2 & k & 1  \\    -k & 3 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow \]               \[k(k-3)-3(2+k)+1(6+{{k}^{2}})=0\] \[\Rightarrow \]               \[{{k}^{2}}-3k-6-3k+6+{{k}^{2}}=0\] \[\Rightarrow \]               \[2{{k}^{2}}-6k=0\] \[\Rightarrow \]               \[k(k-3)=0\] \[\Rightarrow \]               \[k=0,3\]


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