Let \(\vec{a}=2 \hat{i}+\hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}+3 \hat{j}-5 \hat{k}\) be two vectors, and \(\overrightarrow{\mathrm{r}}\) be a vector along the vector \(3 \overrightarrow{\mathrm{a}}-2 \overrightarrow{\mathrm{b}}\) such that \(|\overrightarrow{\mathrm{r}}|=\sqrt{74}\). If the direction of \(\vec{r}\) is opposite to that of \(3 \vec{a}-2 \vec{b}\), then \(\overrightarrow{\mathrm{r}}=\)

1. A \(-7 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\)
2. B \(4 \hat{i}+7 \hat{j}-3 \hat{k}\)
3. C \(-4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}\)
4. D \(4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\)