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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Direction: (Q. Nos. 88) For the following questions, the correct answers from the codes (a), (b), (c) and (d) defined as follows.
    We have, \[a\cdot \,(b\times c)=[\,a\,b\,c]\] Statement I If a, b and c are unit coplanar vectors, then \[[2a-b\,\,\,2b-c\,\,\,2c-a]=0\] Statement II [a b c] = 0

    A)  Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.

    B)  Statement I is true, Statement II is also true and Statement II is not the correct explanation of Statement I.

    C)  Statement I is true, Statement II is false.

    D)  Statement I is false, Statement II is true.

    Correct Answer: A

    Solution :

     Statement I \[[2a-b\,\,2b-c\,\,2c-a]\] \[=(2a-b)\cdot [2b-c)\times (2c-a)]\] \[=(2a-b)\cdot \,[4b\times c-2b\times a-0+c\times a]\] \[=8\,[a\,b\,c]-4\,[\,a\,b\,a]+2\,[a\,\,c\,\,a]\] \[-4\,[b\,b\,c]\,+2\,[b\,b\,a]\,-\,[b\,c\,a]\] \[=8\,[a\,b\,a]\,-\,[b\,c\,a]\,=7\,[a\,b\,c]\] = 0                          \[(\because \,a,b\] and c are coplanars)


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