Suppose

a = a_x i + a_y j + a_z k

b = b_x i + b_y j +b_z k

Then

ab = (a_yb_z - a_zb_y) i + (a_zb_x - a_xb_z) j + (a_xb_y - a_yb_x) k

(1,01) (1,0,1) = 0;

(1,1,1) (1,1,0) = (-1,1,0)       

To check your answer: check that answer is orthogonal to each factor.