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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    If the position vector of A with respect to O is \[3\hat{i}-2\hat{j}+4\hat{k}\]and \[\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k},\] then the position vector of B with respect to 0 is

    A)  \[-\hat{j}+3\hat{k}\]     

    B)  \[6\hat{i}-3\hat{j}+5\hat{k}\]

    C)  \[\hat{j}-3\hat{k}\]      

    D)  \[\hat{i}-3\hat{j}+5\hat{k}\]

    Correct Answer: B

    Solution :

    Given  \[\overrightarrow{OA}\]\[\overrightarrow{OA}=3\hat{i}-2\hat{j}+4\hat{k}\] and \[\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k}\] \[\because \] \[\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}\] \[\therefore \] \[\overrightarrow{OB}=\overrightarrow{AB}+\overrightarrow{OA}\] \[=3\hat{i}-\hat{j}+\hat{k}+3\hat{i}-2\hat{j}+4\hat{k}\] \[=6\hat{i}-3\hat{j}+5\hat{k}\]


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