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

  • question_answer
    The components of a vector a along and perpendicular to the non-zero vector b are respectively            [IIT 1988]

    A)                 \[\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{a}|},\,\frac{|\mathbf{a}\,\times \,\mathbf{b}|}{|\mathbf{a}|}\]       

    B)                 \[\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{b}|},\,\frac{|\mathbf{a}\,\times \,\mathbf{b}|}{|\mathbf{b}|}\]

    C)                 \[\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{a}|},\,\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{a}|}\]     

    D)                 \[\frac{|\mathbf{a}\,\times \,\mathbf{b}|}{|\mathbf{a}|},\,\frac{|\mathbf{a}\,\times \,\mathbf{b}|}{|\mathbf{b}|}\]

    Correct Answer: B

    Solution :

               Component of \[\mathbf{a}\] along \[\mathbf{b}=a\cos \theta =\frac{|\mathbf{a}\,.\,\mathbf{b}|}{|\mathbf{b}|}\]                                 Similarly component of \[\mathbf{a}\] perpendicular to \[\mathbf{b}\] \[=a\sin \theta =\frac{|\mathbf{a}\times \mathbf{b}|}{|\mathbf{b}|}.\]


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