Question

$\overrightarrow{ab}$ and $\overrightarrow{ba}$ name the same ray.
never
always
sometimes

Explanation:

Step1: Recall the definition of a ray

A ray is defined by a starting point and a direction. For a ray \(\overrightarrow{AB}\), the starting point is \(A\) and it extends through \(B\) in the direction away from \(A\) towards \(B\) (and beyond). For a ray \(\overrightarrow{BA}\), the starting point is \(B\) and it extends through \(A\) in the direction away from \(B\) towards \(A\) (and beyond).

Step2: Analyze the directions and starting points

The ray \(\overrightarrow{AB}\) has initial point \(A\) and goes through \(B\), while \(\overrightarrow{BA}\) has initial point \(B\) and goes through \(A\). These two rays have different initial points and different directions (unless \(A = B\), but if \(A = B\), they are not distinct rays). So, in general, \(\overrightarrow{AB}\) and \(\overrightarrow{BA}\) do not name the same ray.

Answer:

A. never