Dot product /cross product question

Question

What are the coordinates of w that is perpendicular to the following vectors:

u=(4,-3,2). V=(8,-4,2)

Answer 1

Let w = (a,b,c) and w•u = 4a - 3b + 2c = 0 and w•v = 8a - 4b + 2c = 0. If we subtract this equations we get

4a - b = 0, so b = 4a; 2c = 3b - 4a = 8a, c = 4a also. We have w = (a, 4a,4a) = a(1,4,4) for any a is perpendicular to u and v.