I've finished this problem and I got the tangent plane equation to be

Fx Fy Fz

Tangent plane(at Xo,Yo,Zo) = yo*zo(x-xo) + xo*zo(y-yo) + xo*yo(z-zo)

Not sure what the problem is asking in terms of the intercept, is it because if you multiply in Fx, Fy, Fz you get xo*yo*zo which would be the intercept?

Thanks!