Find the vector equation for the tangent line to the curve of intersection of x^2+y^2=25 and y^2+z^2=20 at (3,4,2)

Michael gose to a theme park and rides two different roller coasters that both begin on a raised platform his height while on the first roller coaster measured in feet from the platform height can be modeled by the following graph where t is the number of seconds since the ride began