If $\mathbf{a}=2 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are orthogonal, then value of $\lambda$ is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors such that $a+b+c=0$, then the value of $\mathbf{a} \cdot \mathbf{b}+\mathbf{b} \cdot \mathbf{c}+\mathbf{c} \cdot \mathbf{a}$ is equal to