The parametric curves intersect at point (4, 1, 32).
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Using the parametric functions for both r1 and r2 as functions of t, we have that:
Curve 1:
\(x_1(t) = t, y_1(t) = 5 - t, z_1(t) = 48 - t^2\)
Curve 2:
\(x_2(t) = 8 - t, y_2(t) = t - 3, z_2(t) = t^2\)
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They intersect where they are equal, thus:
\(x_1(t) = x_2(t)\)
\(t = 8 - t\)
\(2t = 8\)
\(t = \frac{8}{2}\)
\(t = 4\)
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Using curve 1:
\((x(t), y(t), z(t)) = (t, 5-t, 48 - t^2)\)
Then
\((x(4), y(4), z(4)) = (4, 5-4, 48 - 4^2) = (4, 1, 32)\)
They intersect at point (4, 1, 32).
A similar problem is given at https://brainly.com/question/17426048
