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JEE Main & Advanced Physics Vectors Question Bank Addition and Subtraction of Vectors

  • question_answer
    \[\overrightarrow{A}=2\hat{i}+\hat{j},\,B=3\hat{j}-\hat{k}\] and \[\overrightarrow{C}=6\hat{i}-2\hat{k}\].                 Value of \[\overrightarrow{A}-2\overrightarrow{B}+3\overrightarrow{C}\] would be

    A)                 \[20\hat{i}+5\hat{j}+4\hat{k}\]

    B)                             \[20\hat{i}-5\hat{j}-4\hat{k}\]

    C)                 \[4\hat{i}+5\hat{j}+20\hat{k}\]

    D)                 \[5\hat{i}+4\hat{j}+10\hat{k}\]

    Correct Answer: B

    Solution :

                        \[\overrightarrow{A}-2\overrightarrow{B}+3\overrightarrow{C}=(2\hat{i}+\hat{j})-2(3\hat{j}-\hat{k})+3(6\hat{i}-2\hat{k})\]                 \[=2\hat{i}+\hat{j}-6\hat{j}+2\hat{k}+18\hat{i}-6\hat{k}\]=\[20\hat{i}-5\hat{j}-4\hat{k}\]


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