Chapter 13 - Vector Geometry - 13.1 Vectors in the Plane - Exercises - Page 650: 32

Since $\overrightarrow {AB} $ and $\overrightarrow {PQ} $ have the same components, they are equivalent.

We have $A = \left( {5,8} \right)$ and $B = \left( {1,8} \right)$. So, $\overrightarrow {AB} = \left( {1,8} \right) - \left( {5,8} \right) = \left( { - 4,0} \right)$. We have $P = \left( {1,8} \right)$ and $Q = \left( { - 3,8} \right)$. So, $\overrightarrow {PQ} = \left( { - 3,8} \right) - \left( {1,8} \right) = \left( { - 4,0} \right)$. Since $\overrightarrow {AB} $ and $\overrightarrow {PQ} $ have the same components, they are equivalent.