Find a vector function that represents the curve that is

Question

(1) At what points does the curve <2t, t+5, t²> intersects the paraboloid z = x² +y²

(2) Find a paraboloa that has a curvature of 3 at x = 0.

(3) A force with magnitude 20 N acts directly upward from the xy-plane on an object with mass 4-kg. The object starts at the origin with initial velocity v(0) = i - j. Find the position of the object at time t.

(4) Find a vector function that represents the curve that is the intersection of the cylinder x² + y² = 1 and the hyperboloid z = x² +y².