1. Suppose that an airplane is flying with airspeed of 260 kilometers per hour while a wind is blowing to the west at 100 kilometers per hour. Indicate on a figure the appropriate direction that the plane must follow to fly directly south. What will be the resultant speed? 2. Find e so that the vector v = [!] is orthogonal to w = [-2.1. [2] 3. Find c so that the vector v = cis orthogonal to v = -2 4. If possible, find a, b, and c so that v = b is orthogonal to both w = 12 and x = 0: = ) 5. If possible, find a and b so that v = b is orthogonal to both w = 1 and x = 6. Let be the angle between the nonzero vector u and v in Ror R.Show that if u and v are parallel, thencos 0 = +1. 7. Show that the only vector x in R or R that is orthogonal in every other vector is the zero vector. 8. Let S = {(24]} and T = {[1] {}]} be ordered basis for R. Let v = {E}]} and w = {({]} a. Find the coordinate vectors with respect to the basis T. b. Find the coordinate vectors of v and w with respect to directly? 9. Let S = and T = 00: 0 U170 be ordered bases for R'. Let v = 3 and w= a. Find the coordinate vectors with respect to the basis T. b. Find the coordinate vectors of v and w with respect to S directly? and write 10. Find a basis for the subspace V or "spamed by s ={10E):61-6) "] c) each of the following vectors in terms of the basis vectors. a. 3 4 [12