Determine a vector that is orthogonal to the vector e = [3, -1, 4]
cos 90 = 0 (orthogonal vectors have 90 in between)
substitute a vector [x1 , x2, x3] for the second vector and use dot product
[3, -1, 4] . [x1, x2, x3] = 0
3x1 - x2 + 4x3 = 0
then solve for xs that would work.
an example would be [1, 3, 0]