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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    If\[\mathbf{a,}\,\,\mathbf{b}\]and\[\mathbf{c}\]are non-collinear vectors such that for some scalars\[\text{x,}\,\,\text{y,}\,\,\text{z,}\,\,x\mathbf{a}+x\mathbf{b}+x\mathbf{c}=0\], then

    A) \[x=0,\,\,y=0,\,\,z=0\]

    B) \[x\ne 0,\,\,y\ne 0,\,\,z=0\]

    C) \[x=0,\,\,y\ne 0,\,\,z\ne 0\]

    D) \[x\ne 0,\,\,y\ne 0,\,\,z\ne 0\]

    Correct Answer: A

    Solution :

    Since,\[x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=0\] Also,\[\mathbf{a,}\,\,\mathbf{b}\]and\[\mathbf{c}\]are non-collinear vectors, then\[x=y=z=0\]


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