A) 10 J
B) 12 J
C) 13 J
D) None of these
Correct Answer: C
Solution :
\[{{\vec{r}}_{1}}=\hat{i}+\hat{j}+\hat{k}\] and \[{{\vec{r}}_{2}}=2\hat{i}+3\hat{k}\] \[\therefore \]\[\Delta \vec{r}={{\vec{r}}_{2}}-{{\vec{r}}_{1}}=2\hat{i}+3\hat{k}-\hat{i}-\hat{j}-\hat{k}\] \[=\hat{i}-\hat{j}+2\hat{k}\] \[W=\vec{F}.d\vec{r}\] \[=(3\hat{i}-2\hat{j}+4\hat{k}).(\hat{i}-\hat{j}+2\hat{k})\] \[=3+2+8=13\,J\] Hence, the correction option is[c].
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