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WB JEE Medical WB JEE Medical Solved Paper-2011

  • question_answer
    Given \[\vec{A}=2\hat{i}+3\hat{j}\]and \[\vec{B}=\hat{i}+\hat{j}.\]The component of vector \[\vec{A}\] along vector \[\vec{B}\] is

    A)  \[\frac{1}{\sqrt{2}}\]                                    

    B)  \[\frac{3}{\sqrt{2}}\]

    C)  \[\frac{5}{\sqrt{2}}\]                                    

    D)  \[\frac{7}{\sqrt{2}}\]

    Correct Answer: C

    Solution :

                     The component of vector \[\text{\vec{A}}\]along vector \[\text{\vec{B}}\] would be equal to A- -B- \[\vec{A}.\frac{{\vec{B}}}{|B|}=(2\hat{i}+3\hat{j}).\frac{(\hat{i}+\hat{j})}{|\hat{i}+\hat{j}|}\] \[=(2\hat{i}+3\hat{j}).\frac{(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{(2+3)}{\sqrt{2}}=\frac{5}{\sqrt{2}}\]


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