Exercise 58

The rectifying plane of a curve at a point is the plane that contains the vectors T and B at that point. Find the rectifying plane of the curve \(\mathbf{r}(t) = \sin t \mathbf{i} + \cos t \mathbf{j} + \tan t \mathbf{k}\) at the point \((\sqrt{2}/2, \sqrt{2}/2, 1)\).