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JEE Main & Advanced AIEEE Solved Paper-2007

  • question_answer
    If \[\hat{u}\] and \[\hat{v}\] are unit vectors and \[\theta \] is the acute angle between them, then\[\Lambda _{HCl}^{o}=426.2\text{ }S\text{ }c{{m}^{2}}/equiv\]is a unit vector for       AIEEE  Solved  Paper-2007

    A)  exactly two values of \[\theta \]

    B)  more than two values of \[\theta \]

    C)  no value of \[\theta \]

    D)  exactly one value of \[\theta \]

    Correct Answer: D

    Solution :

    Let\[(2u\times 3v)\]is a unit vector. \[|2u\times 3v|=1\] \[\Rightarrow \]\[6|u|v||\sin \theta |=1\] \[\Rightarrow \]\[\sin \theta =\frac{1}{6}\]                                   \[(\because |u|=|v|=1)\] Since,\[\theta \]is an acute angle. Hence, there is exactly one value of\[\theta \]for which\[(2u\times 3v)\]is a unit vector.


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