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

  • question_answer
    In a triangle ABC, if \[2\overrightarrow{AC}=3\overrightarrow{CB},\] then \[2\overrightarrow{OA}+3\overrightarrow{OB}\] equals                                                [IIT 1988; Pb. CET 2003]

    A) \[5\overrightarrow{OC}\]

    B) \[\frac{1}{3}\,(2\mathbf{i}-2\mathbf{j}+\mathbf{k})\]

    C) \[\,\overrightarrow{OC}\]    

    D) None of these

    Correct Answer: A

    Solution :

    \[2\overrightarrow{OA}+3\overrightarrow{OB}=2(\overrightarrow{OC}+\overrightarrow{CA})+3\,(\overrightarrow{OC}+\overrightarrow{CB})\] \[=5\overrightarrow{OC}+2\overrightarrow{CA}+3\overrightarrow{CB}=5\overrightarrow{OC}\],  \[\{\because \,2\overrightarrow{CA}=-3\overrightarrow{CB}\}\].       


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