# What is the difference between a scalar, a vector, and a unit vector? Can we take the product of two vectors?

Aug 12, 2017

See below.

#### Explanation:

• 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 $\hat{i}$.

• There are many physical quantities which are expressed as the product of two vectors. For example, magnetic force is given as the cross product $\vec{F} = \vec{I} v \times \vec{B}$. Additionally, work is given as the dot product $W = \vec{F} \cdot \vec{d}$.