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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2010

  • question_answer
    If\[\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}\]and\[\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k},\] then the vector in the direction of\[\overrightarrow{a}\]and having magnitude as\[|\overrightarrow{b}|\]is

    A)  \[7(\hat{i}+2\hat{j}+2\hat{k})\]

    B)  \[\frac{7}{9}(\hat{i}+2\hat{j}+2\hat{k})\]

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

    D)  None of these

    Correct Answer: C

    Solution :

     Required vector\[=|\overrightarrow{b}|\hat{a}\] \[=|\overrightarrow{b}|\frac{\overrightarrow{a}}{|\overrightarrow{a}|}\] \[=\sqrt{9+36+4}\frac{(\hat{i}+2\hat{j}+2\hat{k})}{\sqrt{1+4+4}}\] \[=\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})\]


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