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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    \[\overrightarrow{a}=3\,\hat{i}-5\hat{j}\] and \[\overrightarrow{b}=6\,\hat{i}+3\,\hat{j}\] are two vectors and \[\overrightarrow{c}\] is a vector such that \[\overrightarrow{c}=\overrightarrow{a}\times \overrightarrow{b}\] then \[|\overrightarrow{a}|:|\overrightarrow{b}|:|\overrightarrow{c}|\]

    A) \[\sqrt{34}:\sqrt{45}:\sqrt{39}\]

    B)        \[\sqrt{34}:\sqrt{45}:39\]

    C) \[34\text{ }:\text{ }39\text{ }:\text{ }45\]

    D)        \[39\text{ }:\text{ }35\text{ }:\text{ }34\]

    Correct Answer: B

    Solution :

    [b] We have \[\text{\vec{a}}\times \text{\vec{b}}=39\,\vec{k}=\text{\vec{c}}\] \[\text{Also  }\!\!|\!\!\text{ \vec{a} }\!\!|\!\!\text{ =}\,\,\sqrt{34},\text{ }|\vec{b}|\,=\sqrt{45},\text{  }\!\!|\!\!\text{ \vec{c} }\!\!|\!\!\text{ =}\,\text{39 ;}\] \[\therefore \text{ }\!\!|\!\!\text{ \vec{a} }\!\!|\!\!\text{ :}|\vec{b}|\text{: }\!\!|\!\!\text{ \vec{c} }\!\!|\!\!\text{ }=\sqrt{34}:\sqrt{45}:39.\]


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