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a vector u has initial point (−2, 1) and terminal point (3, 5).
write u in the form
u=ai+bj.

You simply subtract from the coordinates of the terminal point to the coordinates of the initial point.
The x-coordinate is represented the unit vector i and the y-coordinate is for unit vector j. So,
vector u = (-2 - 3)i + (1 - 5)j = -5i - 4j