Compute the orientation of X intersect Z in the following examples by exhibiting positively oriented bases at every point. [By convention, we orient the three coordinate axes so that the standard basis vectors are positively oriented. Orient the xy plane so that {(1,0,0), (0,1,0)} is positive and the yz plane so that {(0,1,0), (0,01)} is positive. Finally, orient S^1 and S^2 as the boundary of B^2 and B^3 respectively.]
(a) X = x axis, Z = y axis (in R^2)
(b) X = S^1, Z = y axis (in R^2)
(c) X = xy-plane, Z = z axis ( in R^3)
(d) X = S^2, Z = yz plane (in R^3)
(e) X = S^1 in xy plane, Z = yz plane (in R^3)
(f) X = xy plane, Z = yz plane (in R^3)
(g) X = hyperboloid x^2+y^2-z^2=a^2 with preimage orientation (a>0), Z = xy plane (in R^3)