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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    If \[a=i+2j+3k\]and \[b=i\times (a\times i)+j\times (a\times j)+k\times (a\times k)\]the length of b is equal to

    A) \[\sqrt{12}\]                                      

    B)         \[2\sqrt{12}\]                  

    C)         \[3\sqrt{14}\]                  

    D)         \[2\sqrt{14}\]

    Correct Answer: D

    Solution :

    We have, \[a=i+2j+3k\] \[\therefore \]\[b=i\times (a\times i)+j\,\times \,(a\times j)+k\times (a\times k)\]         ?(i) Now, \[i\times (a\times i)=(i.i)a-(i.a)i\]                 \[=1(i+2j+3k)-(1)i\]                 \[=2j+3k\] Similarly, \[j\times (a\times j)=i+3k\] and \[k\times (a\times k)=i+2j\] \[\therefore \]From Eq. (i), \[b=2j+3k+i+3k+i+2j\]                 \[=2i+4j+6k\] \[\Rightarrow \]               \[|b|=\sqrt{4+16+36}=2\sqrt{14}\]


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