Tangent line to intersecting surfaces
The accompanying figure illustrates this problem:
Suppose two surfaces intersect to form a curve, , and suppose is a point on . How do you find a parametric equation for the line tangent to at ?
To solve the problem, we observe that the tangent line is orthogonal to both and at , and therefore parallel to . The components of and the coordinates of give us equations for the line.
Developed for use with Thomas' Calculus, published by Pearson.