Final answer:
To find vector a representing the segment →ab with points a(-1, 1) and b(3, 2), we calculate the difference in coordinates to get vector a as (4, 1).
Step-by-step explanation:
To find the vector a with representation given by the directed line segment →ab when point a is (-1, 1) and point b is (3, 2), we need to calculate the difference between the coordinates of points b and a. The vector a is obtained by subtracting the coordinates of point a from point b, or in other words, a = b - a. Applying this, we get:
a = (3 - (-1), 2 - 1) = (3 + 1, 2 - 1) = (4, 1).
Thus, the vector a that represents the directed line segment from point a to point b is (4, 1).