Question: In the game of laser tag, you shoot a harmless laser gun and try to hit a target worn at the waist by other players. Suppose you are standing at the origin of a threedimensional coordinate system and that the xy-plane is the floor. Suppose that waist-high is 3 feet above floor level and that eye level is 5 feet above the floor. Three of your friends are your opponents. One is standing so that his target is 30 feet along the x-axis, another lying down so that his target is at the point x = 20, y = 15, and the third lying in ambush so that his target is at a point 8 feet above the point x = 12, y = 30.
(a) If you aim with your gun at eye level, find the vector from your gun to each of the three targets.
(b) If you shoot from waist height, with your gun one foot to the right of the center of your body as you face along the x-axis, find the vector from your gun to each of the three targets.