Chapter 13 - Vector Geometry - 13.2 Vectors in Three Dimensions - Exercises - Page 659: 14

The vectors $\overrightarrow{ AB}$ and $\overrightarrow{ PQ}$ are equivalent.

First, we have $$\overrightarrow{ AB}=B-A=(3,3,3)-(1,1,1)=\langle 2,2,2 \rangle,$$ $$\overrightarrow{ PQ}=Q-P=(3,6,7)-(1,4,5)=\langle 2,2,2 \rangle.$$ Thus, the vectors $\overrightarrow{ AB}$ and $\overrightarrow{ PQ}$ are equivalent.