Que.4 Do the following sums.(A) 1. An airplane is flying at an airspeed of 500 km/h, on a heading of 040. A 150-km/h wind is blowing from a bearing of 120. Determine the ground velocity of the airplane and the direction of flight. 2. Determine the following system is consistent or inconsistent. if possible ,solve the system. 3x+y-2z=18 ,6x-4y+10z=-10 ,3x-5y+10z=10 3. It is important for aerospace engineers to know the vertical and horizontal components of a rocket's velocity. If a rocket is propelled at an initial velocity of 120 m/s at 80 from the horizontal, what are the vertical and horizontal components of the velocity? 4. Find the volume of parallelepiped, defined by the vectors u = [1, 4, 3], v = [2, 5, 6], and w =[1,2,7]. 5. A wrench is used to tighten a bolt. A force of 60 N is applied in a clockwise direction at 80 to the handle, 20 cm from the centre of the bolt. a) Calculate the magnitude of the torque. b) In what direction does the torque vector point? 6. Use the normal vectors of the planes to describe the following system. 2x+5y+3z=0 , x-3y+6z=19 ,3x+2y+9z=-7