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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    If the vectors \[\vec{i}+3\vec{j}-2\vec{k},2\vec{i}-\vec{j}+4\vec{k}\]and \[3\vec{i}+2\vec{j}+x\vec{k}\]are coplanar, then the value of \[x\] is:

    A) \[-2\]                                    

    B)  2

    C)  1                            

    D)  3

    Correct Answer: B

    Solution :

    Vectors \[\vec{i}+3\vec{j}-2\vec{k},\,-2\vec{i}-\vec{j}+4\vec{k}\]and \[3\vec{i}+2\vec{j}+x\vec{k}\] \[\left| \begin{matrix}    1 & 3 & -2  \\    2 & -1 & 4  \\    3 & 2 & x  \\ \end{matrix} \right|=0\] \[1(-x-18)-3(2x-12)-2(4+3)=0\] \[-x-8-6x+36-8-6=0\Rightarrow -7x=-14\] \[x=2\]


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