# dot vs. cross

• Apr 17th 2012, 06:03 PM
delgeezee
dot vs. cross
What is the purpose of the dot product as opposed to the purpose of the cross product?
• Apr 17th 2012, 06:17 PM
skeeter
Re: dot vs. cross
Quote:

Originally Posted by delgeezee
What is the purpose of the dot product as opposed to the purpose of the cross product?

the result of a dot product of two vectors is a scalar ...

work, a scalar quantity of energy, is the dot product of force and displacement vectors

$W = \vec{F} \cdot \vec{\Delta x}$

the result of a cross product of two vectors is another vector ...

torque, a vector quantity, is the cross product of radius and force vectors

$\vec{\tau} = \vec{r} \times \vec{F}$

try a google search ... you'll find many more examples and applications.
• Apr 17th 2012, 06:43 PM
Plato
Re: dot vs. cross
Quote:

Originally Posted by delgeezee
What is the purpose of the dot product as opposed to the purpose of the cross product?

There is a very simple answer and distinction between the two operations.
The dot product operation maps pairs of vectors to a scalar.
The cross product operation maps pairs of vectors to a vector.