use dot product to show that the cross product between two vectors u and v is orthogonal

Question

can you please check my work

Question: let u = and v = , where the six components can be any real number. show,using the dot product, that the cross product uxv is perpendicular to both u = and v =

attempt :

uxv = (u2v3 - u3v2, u3v1-v3u1, u1v2-v1u2>) and u.v = x1x2 + y1y2 + z1z2 i dont