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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2008

  • question_answer
        If\[\overrightarrow{p}=\hat{i}+\hat{j},\overrightarrow{q}=4\hat{k}-\hat{j}\]and\[\overrightarrow{r}=\hat{i}+\hat{k}\]then the unit vector in the direction of\[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\]is

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

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

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

    D)  \[\hat{i}+2\hat{j}+2\hat{k}\]

    Correct Answer: A

    Solution :

                     We have,\[\overrightarrow{p}=\hat{i}+\hat{j},\text{ }\overrightarrow{q}=4\hat{k}-\hat{j}\]and \[\overrightarrow{r}=\hat{i}\,2\hat{r}\] \[\therefore \]  \[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\]                 \[=3(\hat{i}+\hat{j})+(4\hat{k}-\hat{j})-2(\hat{i}+\hat{k})\]                 \[=\hat{i}+2\hat{j}+2\hat{k}\] \[\therefore \]Unit vector of \[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\]                 \[=\frac{\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}}\]                 \[=\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]


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