Find the unit tangent vector at pi/4 for

Question

asked Jun 18, 2024 152k views

1 Answer

Tokfrans · Answer 1 · 2024-06-22T02:25:52+0000

To find the unit tangent vector, differentiate the given vector equation with respect to t and solve for the unit tangent vector.

To find the unit tangent vector, we begin by differentiating the given vector equation with respect to t:

d/dt (Ď + R) = d/dt (-4DĴ)

Using the properties of differentiation, we get:

Ď' + R' = 0

Now, we substitute the given values:

(dĎ/dt, dR/dt) = (0, -4D)

Since dĎ/dt = 0, we have:

dR/dt = -4D

Hence the unit tangent vector is: (-4D/|R|)