Let a = i +2 j +3 k, b =2 i +3 j -5 k and c =3 i - j +λ k be three vectors. Let r be a unit vector along b + c. If r · a =3, then 3 λ is equal to:

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