Final answer:
The domain of the vector function r(t) is (0, infty) since the logarithmic term requires t to be positive.
Step-by-step explanation:
To find the domain of the vector function r(t) = (ln(t^3), t^8 - t^2, 2t), we must determine where the function is defined. The first term, ln(t^3), requires that t^3 must be positive, so t > 0. There are no restrictions on t for the second and third terms of r(t). Hence, the domain of r(t) is t > 0, or in interval notation: (0, infty).