Chapter 12.4, Problem 7E

(a)

To determine

Show that the equation $n\left(t\right)=-g^{\prime }\left(t\right)i+f^{\prime }\left(t\right)j$ and $-n\left(t\right)=g^{\prime }\left(t\right)i-f^{\prime }\left(t\right)j$ are normal to the given curve vector at the point $\left(f\left(t\right),g\left(t\right)\right)$.

(b)

To determine

Find the value of the unit normal vector for the given curve.

(c)

To determine

Find the value of the unit normal vector for the given curve.