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BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer
    If the volume of parallelepiped with\[4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}\]with coterminous edges \[4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}\] and \[3\hat{i}+9\hat{j}+p\hat{k}\]is 34 cubic unit, then? is equal to

    A)  4                            

    B)         -13                        

    C)         13                         

    D)         6

    Correct Answer: B

    Solution :

    Since, coterminus edges of a parallelepiped are \[4\hat{i}+5\hat{i}+\hat{k},-\hat{j}+\hat{k}\]and\[3\hat{i}+9\hat{j}+p\hat{k}\]and Volume of parallelepiped = 34 \[\therefore \]  \[\left| \begin{matrix}    4 & 5 & 1  \\    0 & -1 & 1  \\    3 & 9 & p  \\ \end{matrix} \right|=34\] \[\Rightarrow \]\[4\left| \begin{matrix}    -1 & 1  \\    9 & p  \\ \end{matrix} \right|-5\left| \begin{matrix}    0 & 1  \\    3 & p  \\ \end{matrix} \right|+1\left| \begin{matrix}    0 & -1  \\    3 & 9  \\ \end{matrix} \right|=34\] \[\Rightarrow \]\[4(-p-9)-5(-3)+1(3)=34\] \[\Rightarrow \]\[-4p-36+15+3=34\] \[\Rightarrow \]\[4p=-36+18-34\] \[\Rightarrow \]\[p=-\frac{52}{4}=-13\]


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