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JEE Main & Advanced Physics Vectors Question Bank Multiplication of Vectors

  • question_answer
    The linear velocity of a rotating body is given by \[\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r},\]where \[\overrightarrow{\omega }\] is the angular velocity and \[\overrightarrow{r}\] is the radius vector. The angular velocity of a body is \[\overrightarrow{\omega }=\hat{i}-2\hat{j}+2\hat{k}\] and the radius vector \[\overrightarrow{r}=4\hat{j}-3\hat{k},\] then \[|\overrightarrow{v}|\] is

    A)                 \[\sqrt{29}\]units            

    B)                 \[\sqrt{31}\]units

    C)                 \[\sqrt{37}\]units            

    D)                 \[\sqrt{41}\]units

    Correct Answer: A

    Solution :

                        \[\vec{v}=\vec{\omega }\times \vec{r}\]\[=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    1 & -2 & 2  \\    0 & 4 & -3  \\ \end{matrix} \right|=\hat{i}(6-8)-\hat{j}(-3)+4\hat{k}\]                 \[-2\vec{i}+3\vec{j}+4\vec{k}\]                 \[|\vec{v}|\ =\ \sqrt{{{(-2)}^{2}}+{{(3)}^{2}}+{{4}^{2}}}\]\[=\sqrt{29}\ unit\]


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