A particle moves from position \( \vec{r}_{1}=3 \hat{i}+2 \hat{j}-6 \hat{k} \) to position \( \v...

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A particle moves from position \( \vec{r}_{1}=3 \hat{i}+2 \hat{j}-6 \hat{k} \) to position \( \vec{r}_{2}=14 \hat{i}+13 \hat{j}+9 \hat{k} \) under the action of force \( \mathrm{F}=4 \hat{i}+\hat{j}+3 \hat{k} N \). The work done by this force will be
a. \( 100 \mathrm{~J} \)
b. \( 50 \mathrm{~J} \)
c. \( 200 \mathrm{~J} \)
d. \( 75 \mathrm{~J} \)
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