Vector Algebra

Let \(\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{b}}=2 \hat{i}+3 \hat{j}-5 \hat{k}\) and \(\overrightarrow{\mathrm{c}}=3 \hat{i}-\hat{j}+\lambda \hat{k}\) be three vectors. Let \(\overrightarrow{\mathrm{r}}\) be a unit vector along \(\vec{b}+\vec{c}\). If \(\vec{r} \cdot \vec{a}=3\), then \(3 \lambda\) is equal to: