Finding an equation describing the plane containing t1&t2?

[mr_coffee]

Hello everyone, this problem is very long so if i screw up one part the whole thing is wrong. But I'm pretty sure I'm doing it right...
The last 5 questions asked me to find the tangent of line T1 and T2 to the Curve t1/t2, at the point (1,3,1). So i found everything, and now i have a vector T1 and T2;
T1 = <1+t,3,1+8t>
T2 = <1,3+3t,1-4t>
Now he wants me to find an equation descrbing the plane containing T1 and T2, one way i could do this is to take the cross product of the 2 vectors because they both intersect at the same point, (1,3,1)...but that's not how he wants us to do it, he wants us to use a method with tangent planes and linear approximation but I'm confused on how to do that@! the chapter doesn't talk about that at all...all he says is
We know that any plan passing through the point P(xo,yo,zo) has an eqwuation of the form
A(x-xo) + B(y-yo) + C(z-zo) = 0;
then it says we can rewrite it as z - zo = a(x-xo) + b(y-yo);
Then it says
Suppose f has continuous partial derivatives. An equation of the tangent plane to the surface z = f(x,y) at the point P(xo,yo,zo) is
z-zo = fx(xo,yo)(x-xo) + fy(xo,yo)(y-yo);
note: fx means partial derivative with respect of x;

Any ideas on what i could do ? Thanks@

 

[Fermat]

You seem to have your curve descibed in terms of a parameter, t.

You will have to define the curve as,

z = f(x,y)

If you can do that, then P(xo,yo,zo) is the tangent point. And the tangent plane at this point will contain any tangent vectors at this point.
Work out the partial derivatives, e.g. fx(xo,yo) as numerical values, where fx(xo,yo) is the partial derivative of f wrt x where x = xo and y = yo.

Then fill in that eqn,

z-zo = fx(xo,yo)(x-xo) + fy(xo,yo)(y-yo);

 

[mr_coffee]

thank u! worked great