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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2008

  • question_answer
    If vector \[2\widehat{i}-\widehat{j}+\widehat{k},\widehat{i}+2\widehat{j}-3\widehat{k}\]and \[3\widehat{i}+p\widehat{j}+5\widehat{k}\] are coplanar, find the value of p

    A)  16                

    B)  \[-4\]

    C)  4             

    D)  \[-8\]

    Correct Answer: B

    Solution :

     Vectors are coplanar if       \[\left| \begin{matrix}    2 & -1 & 1  \\    1 & 2 & -3  \\    3 & p & 5  \\ \end{matrix} \right|=0\] \[2(10+3p)+1(5+9)+1(p-6)=0\] \[20+6p+5+9+p-6=0\] \[7p+34-6=0\] \[7p+28=0\] \[7p=-28\] \[p=-\frac{28}{7}=-4\]


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