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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    If \[2i+3j,i+j+k\]and \[\lambda i+4j+2k\]taken in an order are coterminous edges of a parallelepiped of volume 2 cu units, then value of \[\lambda \]is

    A) \[-4\]                                    

    B)  2

    C)  3                                            

    D)  4                            

    Correct Answer: D

    Solution :

    Given, let \[A=2i+3j+0k\] \[B=i+j+k\] \[C=\lambda i+4j+2k\] If A, B, C are the coterminous edges of a parallelepiped then its volume is \[=(A\times B).C\] \[=\{(2i+3j+0k)\times (i+j+k)\}\]                 \[(\lambda \,i+4j+2k)\] \[=(3\,i-2\,j-k).(\lambda \,i+4\,j+2k)\] \[=3\lambda -8-2\] \[=3\lambda -10\] Given volume =2 \[\Rightarrow \]               \[3\lambda -10=2\] \[\Rightarrow \]               \[3\lambda =12\] \[\Rightarrow \]               \[\lambda =4\]


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