JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer The unit vector parallel to the resultant of the vectors \[\vec{A}=4\hat{i}+3\hat{j}+6\hat{k}\] and \[\vec{B}=-\hat{i}+3\hat{j}-8\hat{k}\] is     [EAMCET 2000]

    A)                    \[\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]

    B)                                      \[\frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k})\]

    C)            \[\frac{1}{49}(3\hat{i}+6\hat{j}-2\hat{k})\]               

    D)            \[\frac{1}{49}(3\hat{i}-6\hat{j}+2\hat{k})\]

    Correct Answer: A

    Solution :

                 Resultant of vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\]                    \[\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}=4\hat{i}+3\hat{j}+6\hat{k}-\hat{i}+3\hat{j}-8\hat{k}\]                    \[\overrightarrow{R}=3\hat{i}+6\hat{j}-2\hat{k}\]                    \[\hat{R}=\frac{\overrightarrow{R}}{|\vec{R}|}=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{\sqrt{{{3}^{2}}+{{6}^{2}}+{{(-2)}^{2}}}}=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7}\]

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