Let v = (1,−2, 1) and w = (0, 1,−3) be vectors in R3.
Then how do I find all unit vectors in R3 which are orthogonal to both v and w?
Why not check them yourself? Are they unit vectors? Are their dot products with v and w equal to 0?
Actually, you only need to check with one of your vectors. Since one is the negative of the other, if this is true for one, it will be true for the other.