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

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    The points with position vectors \[10\,\mathbf{i}+3\,\mathbf{j},\,\,12\,\mathbf{i}-5\,\mathbf{j}\] and \[a\,\mathbf{i}+11\,\mathbf{j}\] are collinear, if \[a=\]                                                             [MNR 1992; Kurukshetra CEE 2002]

    A) 8             

    B) 4

    C) 8

    D) 12

    Correct Answer: C

    Solution :

    If given points be \[A,\,\,B,\,\,C\] then \[\overrightarrow{AB}=k(\overrightarrow{BC})\] or \[2\mathbf{i}-8\mathbf{j}=k[(a-12)\mathbf{i}+16\mathbf{j}]\Rightarrow k=\frac{-1}{2}\] Also, \[2=k(a-12)\Rightarrow a=8.\]       


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