JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    Direction: Let a, b and c are three non-coplanar vectors, i.e., \[[a\,b\,c]\,\ne 0\]. The three new vectors \[a',\,\,b'\] and c' defined by the equation \[a'=\frac{b\times c}{[a\,\,b\,\,c]},\,\,b'=\frac{c\times a}{[a\,\,b\,\,c]}\]and\[c'=\frac{a\times b}{[a\,\,b\,\,c]}\] are called reciprocal system to the vectors a, b and c.
    If a, b, c and a', b', c' are reciprocal system of vectors, then the value of\[a\times a'+b\times b'+c\times c'\] is

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

    B)  \[2\,(a'\times b'\times c')\]

    C)  \[\frac{[a\,\,b\,\,c]}{2}\]

    D)  0

    Correct Answer: D

    Solution :

     \[\therefore \,\,a\times a'+b\times b'+c+c'\]\[=\frac{1}{[a\,b\,c]}[a\times (b\times c)+b\times (c\times a)+c\times (a\times b)]\](for cyclic order) \[=\frac{1}{[a\,b\,c]}[0]=0\]

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