A) \[\vec{a}\]
B) \[2\,\vec{a}\]
C) \[3\,\vec{a}\]
D) \[\vec{0}\]
Correct Answer: A
Solution :
We know that, any vector \[\overrightarrow{a}\] can be uniquely expressed in terms of three non-coplanar vectors as \[\overrightarrow{a}=x\,\hat{i}+y\,\hat{j}+z\,\hat{k}\] multiply scalarly in succession by \[\hat{i},\,\hat{j}\] and \[\hat{k}\], we get \[x=a.\,\,\hat{i},\,y=a.\,\,\hat{j},\,z=a\,.\,\,\hat{k}\] \[\therefore \] \[\overrightarrow{a}=(a\,.\,\,\hat{i})\,\,\hat{i}+(a\,.\,\,\hat{j})\,\hat{j}+(a\,\,.\,\,\hat{k})\,\,.\,\,\hat{k}\]
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