Final answer:
The domain of the vector-valued function is t < 0 or t > 0.
Step-by-step explanation:
The domain of a vector-valued function refers to the set of all possible values of the parameter 't' for which the function is defined. In this case, the vector-valued function is given by:
r(t) = t²i + 1/tj + √(1-t)k
To find the domain, we need to consider any restrictions or limitations on the values that 't' can take. In this function, the only restriction is that 't' cannot be zero since 1/t would be undefined. Therefore, the domain of the function is:
Domain: t < 0 or t > 0