Let u = 10i-2j, v= i-j, and w = i + j. Find scalars a and b such that u = av + bw. bEAn airplane is traveling in the direction 35 west of north at 400 kml'hr. Find the component form ofthe velocity of the airplane. assuming that the positive xaxis represents due east and the positive yaxis represents due north. 1-: What is the component form of the velocity of the airplane? {ED {Round the nal answer to one decimal place as needed.) Consider a 800-N weight suspended by two wires as shown in the figure. Find the magnitude and components of the force vectors F, and F2. 25' 40' F2 F 1 800-N | F 1 | =0 (Round the final answer to one decimal place as needed.)Consider a w-N weight suspended by two wires as shown in the accompanying figure. If the magnitude of vector F, is 160 N, find w and the magnitude of vector 47 38 FI F 2 What is the weight, w? W = N (Type an integer or decimal rounded to three decimal places as needed.)A bird flies from its nest 7" km in the d'rection of 30 north ofeast1 where it stops to rest on a tree. It then flies 11 km in the direction due southeast and lands atop a telephone pole. Place an xyooordinate system so that the origin is the bird's nest the xaxis points east. and the yaxis points north. a. At what point is the tree located? I). At what point is the telephone pole located? a. At what point is the tree located? (DD) {Type an exact answer. using radicals as needed.) Suppose that A, B, and C are the comer points of a thin triangular plate of constant C(1,1,3) density shown here. X # A(5,4,0) M B(3,4,0) Y a. Find the vector from C to the midpoint M of side AB. (Simplify your answer.)