A) \[\alpha =2,\beta =2\]
B) \[\alpha =1,\beta =2\]
C) \[\alpha =2,\beta =1\]
D) \[\alpha =2,\beta =1\]
Correct Answer: D
Solution :
[d] \[\therefore \vec{a}\] lies in the plane of \[\vec{b}\] and \[\vec{c}\] \[\therefore \vec{a}=\vec{b}+\lambda \vec{c}\] \[\Rightarrow \alpha \hat{i}+2\hat{j}+\beta \hat{k}=\hat{i}+\hat{j}+\lambda (\hat{j}+\hat{k})\] \[\Rightarrow \alpha =1,2=1+\lambda ,\beta =\lambda \Rightarrow \alpha =1,\beta =1\]
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