# What is the dot product of two vectors that are parallel?

Jan 15, 2015

It is simply the product of the modules of the two vectors (with positive or negative sign depending upon the relative orientation of the vectors).
A typical example of this situation is when you evaluate the WORK done by a force $\vec{F}$ during a displacement $\vec{s}$.
For example, if you have:

Work done by force $\vec{F}$:
$W = | \vec{F} | \cdot | \vec{s} | \cdot \cos \left(\theta\right)$
Where $\theta$ is the angle between force and displacement; the two vectors being parallel can give:

theta=0° and cos(theta)=cos(0°)=1 so:
$W = 5 \cdot 10 \cdot 1 = 50 J$

Or:

theta=180° and cos(theta)=cos(180°)=-1 so:
$W = 5 \cdot 10 \cdot - 1 = - 50 J$