Major tom is on a spacecraft that follows the path γ(t) = (cos 2πt, 5e^(−t^2)sin πt, t) where t is measured in hours, and the x, y and z coordinates are in hundreds of km. as soon as the ship got into orbit the crew in the earth (commonly known as ground control) noticed that the ship had suffered from some damage during takeoff. together, major tom and ground control design a plan to his rescue: there is an international space station at the point (1, 1, 3) and if major tom’s ship can get within 100 km of the station he can then use a mechanism to stop his ship and travel to the space station and perform the repairs. the crew in ground control orders major tom to turn his engines completely off after 2 hours of flight, so the ship will travel following the tangent trajectory starting at that moment. according to their calculations, he eventually will be close enough to repair his ship. (a) find the shortest distance between major tom’s path and the international space station. (b) find the time at which major tom will be at the closest point. (c) will major tom survive?