Answer
Since $\overrightarrow {AB} $ and $\overrightarrow {PQ} $ do not have the same components, they are not equivalent.
Work Step by Step
We have $A = \left( {1,4} \right)$ and $B = \left( { - 6,3} \right)$. So, $\overrightarrow {AB} = \left( { - 6,3} \right) - \left( {1,4} \right) = \left( { - 7, - 1} \right)$.
We have $P = \left( {1,4} \right)$ and $Q = \left( {6,3} \right)$. So, $\overrightarrow {PQ} = \left( {6,3} \right) - \left( {1,4} \right) = \left( {5, - 1} \right)$.
Since $\overrightarrow {AB} $ and $\overrightarrow {PQ} $ do not have the same components, they are not equivalent.
