JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer Unit vector parallel to the resultant of vectors \[\vec{A}=4\hat{i}-3\hat{j}\]and \[\vec{B}=8\hat{i}+8\hat{j}\]will be             [BHU 1995]

    A)  \[\frac{24\hat{i}+5\hat{j}}{13}\]

    B)                                      \[\frac{12\hat{i}+5\hat{j}}{13}\]

    C)            \[\frac{6\hat{i}+5\hat{j}}{13}\]                                       

    D)            None of these

    Correct Answer: B

    Solution :

                 Resultant of vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\]                    \[\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+8\hat{i}+8\hat{j}\]            \[=12\hat{i}+5\hat{j}\]            \[\hat{R}=\frac{\overrightarrow{R}}{|R|}=\frac{12\hat{i}+5\hat{j}}{\sqrt{{{(12)}^{2}}+{{(5)}^{2}}}}\]\[=\frac{12\hat{i}+5\hat{j}}{13}\]


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