(a)

Draw the vectors and .

Graph :

Graph the vectors and .

(b)

Draw the vectors and .

Graph :

Graph the vectors and .

(c)

Find the expression for and unit tangent vector .

Derivatives :

The derivative of a vector function is defined in much the same way as for real valued  functions.

.

Substitute .

 .

Unit tangent vector :

The unit tangent vector .

Substitute .

.

Therefore, and unit tangent vector is .

(d)

Draw the unit tangent vector .

The unit tangent tangent vector is .

Graph :

Graph the vector

(a)

Graph :

Graph of the vectors and .

(b)

Graph :

Graph of the vectors and .

(c) and unit tangent vector is .

(d)

Graph :

Graph of the vector

.