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

  • question_answer
    If a, b, c are position vector of vertices of a triangle \[ABC\], then unit vector perpendicular to its plane is              [RPET 1999]

    A)                 \[a\times b+b\times c+c\times a\]

    B)                 \[\frac{a\times b+b\times c+c\times a}{|a\times b+b\times c+c\times a|}\]

    C)                 \[\frac{a\times b}{|a\times b|}\]

    D)                 None of these

    Correct Answer: B

    Solution :

               Unit vector perpendicular to plane                    \[=\frac{\overrightarrow{AB}\times \overrightarrow{AC}}{|\overrightarrow{AB}\times \overrightarrow{AC}|}\]\[=\frac{(b-a)\times (c-a)\,}{\left| \,(b-a)\times (c-a)\, \right|}\]                                 \[=\frac{a\times b+b\times c+c\times a}{\left| \,a\times b+b\times c+c\times a\, \right|}.\]


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