A) 1
B) -1
C) 0
D) 2
Correct Answer: C
Solution :
Let\[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\]and \[\vec{c}=r\hat{i}+\hat{j}+(2r-1)\hat{k}\] Since, \[\vec{c}\]is parallel to the plane of \[\vec{a}\] and \[\vec{b}\] therefore, \[\vec{a},\vec{b}\]and\[\vec{c}\] are coplanar. \[\therefore \]\[\left| \begin{matrix} 1 & -2 & 3 \\ 2 & 3 & -1 \\ r & 1 & 2r-1 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1(6r-3+1)+2(4r-2+r)+\]\[3(2-3r)=0\] \[\Rightarrow \]\[6r-2+10r-4+6-9r=0\]\[\Rightarrow \]\[r=0\]You need to login to perform this action.
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