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), \[a+2b=-6c\] \[\Rightarrow \] \[a+2b+6c=0\]You need to login to perform this action.
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