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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

  • question_answer
    If \[\vec{p}=\hat{i}=+\hat{j},\vec{q}=4k-\text{ }\hat{j}\] and \[\vec{r}=\hat{i}+\hat{k}\] then the unit vector in the direction of \[3\vec{p}+\vec{q}-2\vec{r}\] 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, \[\vec{p}=\hat{i}+\hat{j},\] \[\vec{q}=4\hat{k}-\hat{j}\] and \[\vec{r}=\hat{i}\,2\hat{i}\] \[\therefore \]  \[3\vec{p}+\vec{q}-2\vec{r}\]                 \[=3(\hat{i}+\hat{j})+(4\hat{k}-\hat{j})-2(\hat{i}+\hat{k})\]                 \[=i+2\hat{j}+2\hat{k}\] \[\therefore \] Unit vector of \[3\vec{p}+\vec{q}-2\vec{r}\]                                 \[=\frac{\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}}\]                                 \[=\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]


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