Final answer:
The domain of the vector function r(t) = (t - 1)ti + sin(t)j + ln(4 - t²)k is (-2, 2).
Step-by-step explanation:
The domain of a vector function is the set of all values of the independent variable for which the function is defined. In this case, we have the vector function r(t) = (t - 1)ti + sin(t)j + ln(4 - t²)k.
To find the domain, we need to consider the restrictions on the values of t that would make the expression undefined. The natural logarithm function ln(x) is only defined for positive values of x, so we need to make sure that 4 - t² > 0. Solving this inequality, we get -2 < t < 2. Therefore, the domain of r(t) is (-2, 2).