Question

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?