A) i
B) k
C) j
D) i + j + k
Correct Answer: A
Solution :
Let \[\mathbf{a}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\]. Then \[\mathbf{a}\,.\,\mathbf{i}=(x\mathbf{i}+y\mathbf{j}+z\mathbf{k})\,.\,\mathbf{i}=x\] and \[\mathbf{a}\,.\,(\mathbf{i}+\mathbf{j})=x+y\] and \[\mathbf{a}\,.\,(\mathbf{i}+\mathbf{j}+\mathbf{k})=x+y+z\] \[\because \] Given that \[x=x+y=x+y+z\] Now\[x=x+y\,\,\,\Rightarrow y=0\]and \[x+y=x+y+z\,\,\Rightarrow \,\,z=0\] Hence \[x=1\]; \[\therefore \,\,\mathbf{a}=\mathbf{i}\].
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