We are given a curve y = f(x). The position vector at any point (x, y) is r = x i + y j & the tangent vector at that point is t = dx i + dy j. It is known that the position and tangent vectors are perpendicular to each other for the given curve. 1. Write an expression for the dot product r . t. 2. Show that it leads to x dx + y dy = 0. 3. Show that the first order differential equation in (2) has the solution x2 + y2 = c