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Answer : curve r(t) = t i + (2t - t 2)k intersect the paraboloid z = x 2 + y 2
By the equation of r(t), x = t, y = 0, and z = .
Thus, z =
on solving we get,
=
Now, we can solve for t
= 0
So, = 0
2t ( t - 5/2) = 0
t = 0 , t = 5
plugging these values in t = 0 into r(t)
r(0) = <0 , 0 , 0>
r(5) = < 5, 0 , 25 >