Chapter 13.4, Problem 7E

(a)

To determine

To show: The curves $n\left(t\right)=-g^{\prime }\left(t\right)i+f^{\prime }\left(t\right)j\text{ and }-n\left(t\right)=g^{\prime }\left(t\right)i-f^{\prime }\left(t\right)j$ are both normal to the curve $r\left(t\right)=f\left(t\right)i+g\left(t\right)j$ at the point $\left(f\left(t\right),g\left(t\right)\right)$.

(b)

To determine

The principal unit normal N for the curve $r\left(t\right)=ti+e^{2t}j$.

(c)

To determine

The principal unit normal N for the curve $r\left(t\right)=\sqrt{4-t^2}i+tj$.