JEE Main & Advanced AIEEE Solved Paper-2004

  • question_answer
    Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector \[a+2b\]is collinear with c and\[b+3c\]is collinear with a\[(\lambda \]being some non-zero scalar), then \[a+2b+6c\]equals

    A) \[\lambda a\]

    B)                        \[\lambda b\]                   

    C)        \[\lambda c\]   

    D)        0

    Correct Answer: D

    Solution :

    If\[a+2b\]is collinear with c, then \[a+2b=tc\]                       ...(i) Also, if\[b+3c\]is collinear with a, then \[b+3c=\lambda a\]                        ...(ii) \[\Rightarrow \]               \[b=\lambda a-3c\] On putting this value in Eq. (i), we get \[a+2(\lambda a-3c)=tc\] \[\Rightarrow \]               \[a+2\lambda a-6c=tc\] \[\Rightarrow \]               \[(a-6c)=tc-2\lambda a\] On comparing the coefficients of a and b, we get \[1=-2\lambda \] \[\Rightarrow \]               \[\lambda =-\frac{1}{2}\] and        \[-6=t\] \[\Rightarrow \]               \[t=-6\] From Eq. (i), \[a+2b=-6c\] \[\Rightarrow \]               \[a+2b+6c=0\]

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