Let \(\vec{a}, \vec{b}, \vec{c}\) be co-initial vectors and \(\vec{a}=2 \hat{i}-\hat{j}+5 \hat{k}\) and \(\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}-\hat{\mathrm{k}}\). Let \((\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}})=\theta\) be an acute angle and \(\overrightarrow{\mathrm{c}}\) be the vector along the bisector of the angle \(\theta\). If \(\lambda, x\), \(\mathrm{y} \in \mathbb{R}\), then \(\overrightarrow{\mathbf{c}}=\)

1. A \(\lambda(5 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})\)
2. B \(\lambda(-\hat{\mathrm{i}}-8 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})\)
3. C \((2 x+3 y) \hat{i}+(7 y-x) \hat{j}+(5 x-y) \hat{k}\)
4. D \((2 x+3 y) \hat{i}+(x+7 y) \hat{j}+(5 x+y) \hat{k}\)