OK here we go.
Calculate the orthogonal projection of points A(3,5,-1) and B(-4,2,6) onto the plane -2x+4y-z=3
r = a + tb
<X,Y,Z> = <3,5,-1> + t<-2,4,-1>
X = 3 - 2t
Y = 5 + 4t
Z = -1 -t
aX +bY +cZ = d
-2(3 - 2t) + 4(5 + 4t) - ((-1) - t) = 3
t ends up as -18/21 this time
I...