Find three mutually orthogonal unit vectors in r^3 besides plusminus i, plusminus j, and plusminus k. there are multiple ways to do this and an infinite number of answers. for this problem, we choose a first vector u randomly, choose all but one component of a second vector v randomly, and choose the first component of a third vector w randomly. the other components x, y, and z are chosen so that u, v, and w are mutually orthogonal. then unit vectors are found based on u, v, and w. start with u = (1, 1, 2), v = (x, - 1, 2), and w = (1, y, z). the unit vector based on u is (type exact answers, using radicals as needed.)