Question

Can a cross product be Negative

Answer 1

Yes, the cross product be negative

When we find the cross-product of two unit vectors, then the magnitude of the resultant vector is sine and hence always positive. But in the case of the dot product

of two unit vectors, the resultant vector is a cosine that can be negative or positive. If we have to answer it with respect to an angle then we say that if the angle between ${180}^0<a<{360}^0$, then the cross product becomes negative because for ${180}^0<x<{360}^0$,$\sin a$ is negative.

Hence we can say that the cross product be negative

Therefore the answer is Yes, the cross-product is negative.