A) \[Q(a{{e}_{1}}+b{{e}_{2}})\]
B) \[Q\sqrt{{{\left( a{{e}_{1}} \right)}^{2}}+{{\left( b{{e}_{2}} \right)}^{2}}}\]
C) \[Q({{e}_{1}}+{{e}_{2}})\sqrt{{{a}^{2}}+{{b}^{2}}}\]
D) \[Q(\sqrt{e_{1}^{2}+e_{2}^{2})}\ (a+b)\]
Correct Answer: A
Solution :
By using \[W=Q\,(\overrightarrow{E}.\Delta \overrightarrow{r\,})\] Þ\[W=Q\,[({{e}_{1}}\hat{i}+{{e}_{2}}\hat{j}+{{e}_{3}}\hat{k}).(a\hat{i}+b\hat{j})]=Q\,({{e}_{1}}a+{{e}_{2}}b)\]
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