2. We have two vectors that line in the x-y plane. If we take the cross-product of those two

vectors we know that
a. the magnitude of the cross-product will always be equal to the product of the
magnitudes of the two vectors.
b. the magnitude of the cross-product will always be greater than the product of the
magnitudes of the two vectors.
c. the magnitude of the cross-product will always be less than the product of the
magnitudes of the two vectors.
d. the cross-product vector will be perpendicular to the first vector and in the x-y
plane.
e. the cross-product vector will be in either the +z or -z direction.

Is the answer E

yes, since it is perpendicular to both vectors.

Yes, the answer is E. The cross-product of two vectors in the x-y plane will always result in a vector that is perpendicular to the x-y plane, and hence, it will be in either the +z or -z direction.

To understand why this is the case, we can use the right-hand rule. When you place your right hand with your thumb pointing in the direction of the first vector and your fingers pointing in the direction of the second vector, your palm will be facing in the direction of the resulting cross-product vector. Since your palm is perpendicular to the x-y plane, the cross-product vector will also be perpendicular to the x-y plane.