1a. Find the tangent vector r'(t) at the point where t = 3 given r(t) = (5cos(πt))i + (2sin(πt))j + (2t)k.
1b. Find the unit tangent vector, the principal normal vector, and an equation in x, y, z for the osculating plane at the point where t = 1 on the curve r1(t) = (6)i + (8t)j + (4t^2)k.
1c. Find the unit tangent vector, the principal normal vector, and an equation in x, y, z for the osculating plane at the point where t = π/4 on the curve r1(t) = (3cos(2t))i + (3sin(2t))j + (2t)k.