Part 5/6:
- The square root ( \sqrt{3 - t} ) is only defined when ( 3 - t \geq 0 ), implying ( t \leq 3 ).
Combining these findings, we conclude that our vector function ( \mathbf{R}(t) ) is defined in the interval:
[
0 \leq t < 3
]
This suggests that we can compute the output of ( \mathbf{R}(t) ) for any ( t ) within this interval while observing the constraints placed on it due to the square root function.