Let x and y be two perpendicular unit vectors. (a) Find a formula for the magnitude of an arbitrary linear combination ax + by of x and y in terms of a and b. (b) Find the precise condition on a, b, c and d under which the linear combinations ax + by and ex + dy are perpendicular. A purely geometric proof will not receive full credit; try to use vectors! Hint(s): If you aren't sure, try X = (8 ) and y = (9) and see what formula you get. How can you show the same thing works in general