1. Chapter 14 Section 14.3 Curves

2. x y z To get the equation of the line we need to know two things, a direction vector d and a point on the line P. To find d find the derivative and plug in 3 in the derivative. To find P plug 3 into the original function.

3. x y z

4. Motion, Velocity vector and Speed The derivative of the position vector, is called the velocity vector. The length of this vector is called the speed. Remember velocity is a vector giving direction speed is a scalar. Unit Tangent Vector To measure only the change in the direction of a curve we use the unit Tangent vector T. This is a unit vector pointing in the direction of the velocity vector. Unit Normal Vector If we take the derivative of the unit tangent vector and make it of length 1 point in the same direction we call this the unit Normal vector N. This is a unit vector perpendicular to the unit tangent vector.