A) 6 J
B) 13 J
C) 15 J
D) 9 J
Correct Answer: D
Solution :
[d] Given :\[\vec{F}=3\hat{i}+\hat{j}\] \[{{\vec{r}}_{1}}=\left( 2\hat{i}+\hat{k} \right),\,\,{{\vec{r}}_{2}}=\left( 4\hat{i}+3\hat{j}-\vec{k} \right)\] \[{{\vec{r}}_{1}}={{\vec{r}}_{2}}-{{\vec{r}}_{1}}=\left( 4\hat{i}+3\hat{j}-\vec{k} \right)-\left( 2\hat{i}+\hat{k} \right)\] \[\operatorname{or} \vec{r} = 2\hat{i}+3\hat{j} - 2\hat{k}\] So work done by the given force \[\operatorname{w} = \vec{f}\,.\,\vec{r}\] \[= (3\hat{i}+\hat{j}).(2\hat{i}+3\hat{j}-2\vec{k})=6+3=9J\]
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