Problem 1

Consider the curve parameterized by the vector function where .

(a). Find the Curvature at the point

(b). Find the Principal Normal Vector at the point

(c). Find the Coordinates of the Centre of the Osculating Circle at the point

Problem 2

Which of the following vector valued functions parameterize the semi-circle , , oriented in the clockwise direction?

• [x] A. for .
• [ ] B. for .
• [x] C. for .
• [x] D. for .
• [ ] E. for .
• [x] F. for .