Final answer:
The domain of the function r(t) = t² i-j+ln(t-1) k is all real numbers greater than 1, expressed as (1, +∞) in interval notation.
Step-by-step explanation:
The domain of the function r(t) = t² i-j+ln(t-1) k consists of all the values of t for which the function is defined. In this case, since there is a natural logarithm function involved, ln(t-1), we must ensure that the argument (t-1) is positive. The natural logarithm function is undefined for non-positive numbers, which means t-1>0 or t>1. Therefore, the domain of r(t) is all real numbers greater than 1. In interval notation, this is (1, +∞).