1. Let a curve in 3-space be defined by the two equations Show that the two equations define a…

1. Let a curve in 3-space be defined by the two equations  Show that the two equations  define a tangent vector to the curve. (We write “a tangent vector” rather than “the tangent vector” because  is not necessarily of unit magnitude like the tangent vector defined in Eq. (1.9).

2. Prove that if L' is defined by (2.36), then Eq. (2.28) implies Eq. (2.37).