JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector or Cross product of two vectors and its application

  • question_answer
    If q be the angle between the vectors a and b and \[|\mathbf{a}\times \mathbf{b}|\,=\mathbf{a}\,.\,\mathbf{b},\] then \[\theta =\]                   [RPET 1990; MP PET 1990; UPSEAT 2003]

    A)                 \[\pi \]     

    B)                 \[\frac{\pi }{2}\]

    C)                 \[\frac{\pi }{4}\]

    D)                 0

    Correct Answer: C

    Solution :

               \[|\mathbf{a}\times \mathbf{b}|=(\mathbf{a}.\mathbf{b})\Rightarrow ab\sin \theta =ab\cos \theta \]                                 \[\Rightarrow \tan \theta =\frac{ab}{ab}=1\Rightarrow \theta =\frac{\pi }{4}\].


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