At how many points do the space curves $r_1(t) = \langle t^2, 1 - t^2, t + 1 \rangle$ and $r_2(s) = \langle 1 - s^2, s, s \rangle$ intersect?
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Determine whether the space curves given by $\mathbf{r}_{1}(t)=\left\langle t, t^{2}, t+1\right\rangle$ and $\mathbf{r}_{2}(s)=\langle\sqrt{s}, s, s-1\rangle$ intersect, and if they do, determine where.
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