Grade 12 math: vector equations of a plane

the plane with equation r = (1, 2, 3) +m(1, 2, 5) + n(1, -1, 3) intersects the y and z-axes at the points A and B respectively. Determine the equation of the line that contains these two points.

answer: r = (0, 3, 0) + s(0, 3, 2)

I don't how the direction vector is (0, 3, 2); I got r = (0, 3, 0) + s(0, -3, -2) as my answer. I had A (0, 3, 0) and B(0, 0 , -2). Am I wrong?

Points on the y-axis have x and z coordinates zero, while points on the z-axis have x and y coordinates zero. Therefore the intersection with the y-axis is given by the equations
1+m+n=0
3+5m+3n=0.
It is easy to see that the solution is m=0, n=-1. Therefore A is the point (0,3,0).
Similarly, B is obtained by the following equations.
1+m+n=0
2+2m-n=0
giving us m=-1 and n=0 and therefore B is (0, 0, -2).
Since the line goes through A and B, a direction vector is the vector from B to A which is
(0,3,0)-(0,0,-2)=(0,3,2). Since the line goes through A we therefore have its equation to be
r = (0,3,0)+s(0,3,2).
Note that this form is not unique but depends on the choice of the parameter s.

Congratulations, you are absolutely correct, the direction vector is (0 ,-3, -2) which is in the opposite direction to ( 0,3 2), but this does not matter, an answer of r = (0,3,0) + s (0,-3,-2) is just as correct as the answer given,