Determine the unit tangent vector to the curve whose parametric equations are: x=3cos t, y=3sin t, z=4t at the point (1, 2, 1).

Here are the solutions to the problems: 1. (a) Determine the unit tangent vector to the curve whose parametric equations are: x=3 t, y=3 t, z=4t at the point (1, 2, 1). Step 1: Define the position vector r(t). r(t) = 3 t, 3 t, 4t Step 2: Find the derivative of the position vector, r'(t). This is the tangent vector. r'(t) = (d)/(dt) 3 t, 3 t,