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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    If\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]taken in order, is:

    A)  \[{{z}_{1}}-{{z}_{2}}+{{z}_{3}}\]

    B)         \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\]              

    C)         \[\frac{1}{3}({{z}_{1}}-{{z}_{2}}+{{z}_{3}})\]

    D)         \[\frac{1}{3}({{z}_{1}}+{{z}_{2}}-{{z}_{3}})\]

    E)  \[\frac{1}{3}({{z}_{1}}-{{z}_{2}}-{{z}_{3}})\]

    Correct Answer: A

    Solution :

    Let z be the fourth vertex of parallelogram, then \[\frac{{{z}_{1}}+{{z}_{3}}}{2}=\frac{{{z}_{2}}+z}{2}\] \[\Rightarrow \]               \[z={{z}_{1}}+{{z}_{3}}-{{z}_{2}}\]


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