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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    If \[\overset{\to }{\mathop{c}}\,\] is the unit vector perpendicular to both the vectors \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\], then what is another unit vector perpendicular to both the vectors \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,?\]

    A) \[\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{a}}\,\]

    B) \[\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{b}}\,\]

    C) \[-\frac{\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right)}{\left| \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right|}\]

    D) \[\frac{\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right)}{\left| \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right|}\]

    Correct Answer: D

    Solution :

    [d] Let \[\overset{\to }{\mathop{c}}\,\] is the unit vector perpendicular to both the vectors \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\]. So, A unit vector which is perpendicular to both the vectors \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\] is \[\frac{\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right)}{\left| \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right|}\]


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