Vector Algebra

Let $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ be the position vectors of four points $A, B, C$ and $D$ respectively. If a point $P$ divides $A B$ in the ratio $2: 1$ internally and a point $Q$ divides $C D$ in the ratio $1: 2$ externally, then the ratio in which the point with position vectors $5 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ divides $P Q$ is