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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    If\[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]are position vectors of the vertices of the triangle ABC, then\[\frac{\left| \left( \overrightarrow{a}-\overrightarrow{c} \right)\times \left( \overrightarrow{b}-\overrightarrow{a} \right) \right|}{\left( \overrightarrow{c}-\overrightarrow{a} \right).\left( \overrightarrow{b}-\overrightarrow{a} \right)}\]is equal to

    A)  \[cot\text{ }A\]                               

    B)  \[cot\,C\]

    C)  \[-tanC\]            

    D)         \[tan\,C\]

    E)  \[tan\text{ }A\]

    Correct Answer: E

    Solution :

    Now \[\frac{|(\overrightarrow{a}-\overrightarrow{c})\times (\overrightarrow{b}-\overrightarrow{a})|}{(\overrightarrow{c}-\overrightarrow{a}).(\overrightarrow{b}.\overrightarrow{a})}\] \[=\frac{|\overrightarrow{AC}\times \overrightarrow{BA}|}{\overrightarrow{AC}.\overrightarrow{BA}}=\frac{||\overrightarrow{AC}||\overrightarrow{BC}|\sin A\hat{n}|}{|\overrightarrow{AC}||\overrightarrow{BC}|\cos A}\] \[=\tan A\]


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