Find a vector parametric equation for the plane containing the points whose position vectors are
u = (1,−1, 0), v = (3, 0,−4) and w = (0, 2, 5).
Find our direction vectors
u,w = (0-1, 2 - -1, 5-0) = (-1, 3, 5)
u,v = (3-1, 0 - -1, -4 -0) = (2, 1, -4)
Now that we found the direction vectors, we need only apply one of the three points we already have to find our equation of the plane
(x, y, z) = (1, -1, 0) + r(2, 1, -4) + s(-1, 3, 5)