A) \[z\mathbf{i}-x\mathbf{k}\]
B) 0
C) \[y\mathbf{j}\]
D) \[-z\mathbf{i}+x\mathbf{k}\]
Correct Answer: A
Solution :
Since \[\mathbf{a},\,\mathbf{b},\,\mathbf{c}\] form a right handed system \[\therefore \,\mathbf{c}=\mathbf{b}\times \mathbf{a}=\mathbf{j}\times (x\mathbf{i}+y\mathbf{j}+z\mathbf{k})\] \[=x(\mathbf{j}\times \mathbf{i})+z(\mathbf{j}\times \mathbf{k})=-x\mathbf{k}+z\mathbf{i}=z\mathbf{i}-x\mathbf{k}\].
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