MATH 211 Lecture Notes - Lecture 12: Tangent Vector, Tangent, Unit Vector

• School: BRCC
• Department: MATH - Mathematics
• Course: MATH 211
• Professor: William F.Bertolette

Document Summary

Math 212 section 12. 4 tangent vectors and normal vectors. Learning objective: the learner will be able to (1) find a unit tangent vector and a principal unit normal vector. Find the unit tangent vector to the curve given by (cid:4666)(cid:4667)= (cid:2835) + (cid:2870) (cid:2836) when t = 1. The tangent line to a curve at a point is the line that passes through the point and is parallel to the unit tangent vector. Example 2: finding the tangent line at a point on a curve helix given by. Find (cid:4666)(cid:4667) and then find a set of parametric equations for the tangent line to the. (cid:4666)(cid:4667)=(cid:884)cos(cid:2835) + (cid:884)sin (cid:2836) + at the point (cid:4672) (cid:884), (cid:884), (cid:2872) (cid:4673). The tangent line to a curve at a point is determined by the unit tangent vector at the point. In example 2, there are infinitely many vectors that are orthogonal to the tangent vector (cid:4666)(cid:4667). One of these is the vector (cid:4666)(cid:4667).