Calculus

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Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2

I took the cross product of the 2 equations and got 3i-j-2k

I then set z=0 and got x=5/2 and y=1/2.
I got:
x=5/2 +3t
y=1/2-t
z=-2t

However, the answers are supposed to be:
x=5/2-(3/2)t
y=1/2+(1/2)t
z=t

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