On uses the right hand rule: the first vector goes to the thumb, the second vector goes to the index finger, then the cross product is given perpendicular to the both as the middle finger. If one changes the sequence of the vectors, the middle finger directs to the reverse direction - move your hand, do not crash joints.

The dot product and the VectorAngle do not mark the sequence of input vectors

In[41]:= VectorAngle[ {2, -1, 1}, {3, 2, 1}] == VectorAngle[ {3, 2, 1}, {2, -1, 1}]
Out[41]= True

In[42]:= Dot[ {2, -1, 1}, {3, 2, 1}] == Dot[ {3, 2, 1}, {2, -1, 1}]
Out[42]= True

the cross product does

In[46]:= Sign[Cross[ {2, -1, 1}, {3, 2, 1}]]
Out[46]= {-1, 1, 1}

In[43]:= Sign[Cross[ {2, -1, 1}, {3, 2, 1}]] == -Sign[Cross[ {3, 2, 1}, {2, -1, 1}]]
Out[43]= True

note that there is no single sign of a vector, it really just the right hand rule.

If you want to know, whether the angle is right, use VectorAngle

In[49]:= VectorAngle[ {1, 2, 3}, {-2, 1, 0}]
Out[49]= \[Pi]/2

that's a right angle.