What is the difference between a scalar, a vector, and a unit vector? Can we take the product of two vectors?
A scalar quantity has magnitude but no direction. An example of a scalar quantity is density.
A vector quantity has both magnitude and direction. An example of a vector quantity is force.
A unit vector is a vector with magnitude
#1#. An example of a unit vector is #hati#.
There are many physical quantities which are expressed as the product of two vectors. For example, magnetic force is given as the cross product
#vecF=vecIvxxvecB#. Additionally, work is given as the dot product #W=vecF*vecd#.