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.