## Basis of tangent space of a sphere

Let S be the two-dimensional sphere in R3. For a given x∈S, i.e. ‖, I would like to find basis vectors b_1(x) and b_2(x) that span the tangent space of S a the point x. My first try was something like b_1(x) = (x_2, -x_1, 0)^T and b_2(x) = (0, x_3, -x_2)^T but that is … Read more