Question

Find the equation of the tangent plane

Answer 1

Suppose you need to know an equation of the tangent plane to a surface S at the point
P(2, 1, 3).
You don't have an equation for S but you know that the curves
\[r_1(t)=< 2 + 3t, 1 − t2, 3 − 5t + t2 >\]\[r_2(t) = < 1 + u2, 2u3 − 1, 2u + 1 >\] both lie on S. Find an equation of the tangent plane at P.