Python: Setting the X and Y vectors of a bullet

I need to calculate the vector_x and vector_y of a bullet, fired from x1, y1. The target is at x2, y2.

vector_x describes the number of units the bullet travels in the x direction per second. vector_y describes the same, just with the y direction.

I tried many different versions of the same function, but I was unable to come up with a version that:

Keeps vector_x and vector_y between 0 and 1
The bullets hit the target (assuming inaccuracy is 0), no matter where the target is.
Inaccuracy has the same hit chance no matter where the target is relative to x1, x1.

x 0, y 0 is at the top left corner.

This is my best attempt so far:

def get_vectors(x1, y1, x2, y2, inaccuracy=0):
    x2 += random.randint(inaccuracy * -1, inaccuracy)
    y2 += random.randint(inaccuracy * -1, inaccuracy)

    x_dist = x2 - x1
    y_dist = y2 - y1

    dist = [x_dist, y_dist]


    if x_dist >= 0:
        if y_dist >= 0:  # BOTH POSITIVE
            vector_x = x_dist / max(dist, key=abs)
            vector_y = y_dist / max(dist, key=abs)
        else:  # X POSITIVE Y NEGATIVE
            vector_x = x_dist / max(dist, key=abs) * -1
            vector_y = y_dist / max(dist, key=abs) * -1
    else:
        if y_dist >= 0:  # X NEGATIVE Y POSITIVE
            vector_x = x_dist / max(dist, key=abs)
            vector_y = y_dist / max(dist, key=abs)
        else:  # BOTH NEGATIVE
            vector_x = x_dist / max(dist, key=abs) * -1
            vector_y = y_dist / max(dist, key=abs) * -1

    return vector_x, vector_y

While this works in some cases, it mostly fires in wrong directions. How can I fix this code?

Answer

A simple unit vector approach:

def get_vector(x1, y1, x2, y2) -> tuple[int, int]:
    
    # Vector v or difference
    v_x = x2 - x1
    v_y = y2 - y1
    
    # TODO: Add inaccuracy to v


    # lenght of v
    v_len = (v_x**2 + v_y**2)**0.5
    
    # unit vector u of v
    u_x = v_x / v_len
    u_y = v_y / v_len
    
    return (u_x, u_y)

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Answer