Example 2: Tangent Line of a Spiral

Find the vector equation of the tangent line for the spiral

F(t) = cos ti + sin tj + ¼tk

at the point t = π/3. The derivative is

F'(t) = - sin ti + cos tj + ¼k.

At t = π/3 the tangent line has the equation

X = F(π/3) + tF'(π/3)

or

The tangent line is shown in Figure 10.7.2.

Figure 10.7.2