Final answer:
The curves r₁(t) = (t, 2- t, 24 + t²) and r₂(s) = (6 - s, s - 4, s²) intersect when their coordinates are equal. By setting up equations and solving them, we can find the values of t and s where the curves intersect.
Step-by-step explanation:
The curves r₁(t) = (t, 2- t, 24 + t²) and r₂(s) = (6 - s, s - 4, s²) intersect when their coordinates are equal. Therefore, we can set up the following equations:
t = 6 - s
2 - t = s - 4
24 + t² = s²
Simplifying and rearranging these equations, we get:
t + s = 6
t + s = 6
t² - s² = -24
Solving these equations, we find the values of t and s where the curves intersect.