From my understanding from university physics from Pearson (Page ~20):
Dot product multiplies "like" unit vector terms and cross product multiplies "unlike" unit vector terms. So, why does the cross product retain its unit vector (ñ), but dot product does not?
$A\cdot B = AB\cos(\theta) =$ magnitude of $A$ * The component of $B$ that is parallel to $A$.
So shouldn't the unit vector be going in the direction of $A$? Do mathematicians drop unit vectors when stuff only goes in one direction and then call it a scalar?