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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If O be the circumcentre and O' be the orthocentre of the triangle ABC, then \[\overrightarrow{O'A}+\overrightarrow{O'B}+\overrightarrow{O'C}=\]

    A) \[\overrightarrow{OO}'\]     

    B) \[2\,\overrightarrow{O'O}\]

    C) \[2\,\overrightarrow{OO'}\] 

    D) 0

    Correct Answer: B

    Solution :

    \[\overrightarrow{{O}'A}=\overrightarrow{{O}'O}+\overrightarrow{OA}\] \[\overrightarrow{{O}'B}=\overrightarrow{{O}'O}+\overrightarrow{OB}\] \[\overrightarrow{{O}'C}=\overrightarrow{{O}'O}+\overrightarrow{OC}\] \[\Rightarrow \overrightarrow{{O}'A}+\overrightarrow{{O}'B}+\overrightarrow{{O}'C}\] \[=3\overrightarrow{{O}'O}+\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}\] Since \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}=\overrightarrow{O{O}'}=-\overrightarrow{{O}'O}\] \[\therefore \] \[\overrightarrow{{O}'A}+\overrightarrow{{O}'B}+\overrightarrow{{O}'C}=2\overrightarrow{{O}'O}\].


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