(1) Let 17 = i 2j + 2k. Find the scalar c such that the length of 11' = 017 is 12 and that 11', 17' are in opposite directions. Round the nearest hundredth. (2) A submarine climbs at an angle of arr/6 radians (30) above the horizontal with a heading to the northeast. If its speed is 20 knots, nd the component of the veloc- ity (in knots) in the zit-direction, using the standard convention that the positive a: direction is east, the positive :1; direction is north, and the positive 2: direction is up. Round to the nearest hundredth. (3) A plane at cruising altitude heads due east at 600 mph while experiencing a 30 mph wind blowing 30 east of north. What is the plane's groundspeed in mph, which is the speed as observed from the ground? Round to the nearest tenth. Hint: Speed is the magnitude of velocity. (4) A IOU-lb block hangs at rest from cables as shown in the picture below: 1! = (0, 100) Find the magnitude of the force Ff; in lbs to the nearest hundredth. Hints. FA ( FAsin (6), F13 cos (9)) and F3 (F3 sin (7), F3 cos (7)) where FA, F3 are the magnitudes of FA, F3 respectively and 0,7 are the angles between the vectors FA, F3 and the upward direction respectively Since the object is at rest, the sum of all forces has to be 0