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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If the position vectors of the points A, B, C be \[\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}\] and \[a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}\] respectively, then the points A, B, C are collinear if

    A) \[a=b=c=1\]

    B) \[a=1,\,\,b\] and \[c\] are arbitrary scalars

    C) \[a=b=c=0\]

    D) \[c=0,\,\,a=1\] and b is arbitrary scalars

    Correct Answer: D

    Solution :

    Here \[\overrightarrow{AB}=-2\mathbf{j},\] \[\overrightarrow{BC}=(a-1)\mathbf{i}+(b+1)\mathbf{j}+c\mathbf{k}\] The points are collinear, then \[\overrightarrow{AB}=k\,(\overrightarrow{BC})\] \[-2\mathbf{j}=k\{(a-1)\mathbf{i}+(b+1)\,\mathbf{j}+c\mathbf{k}\}\]  On comparing, \[k\,(a-1)=0\], \[k(b+1)=-2,\] \[kc=0\]. Hence \[c=0,\] \[a=1\] and \[b\]is arbitrary scalar.           


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