# Math Help - dot vs. cross

1. ## dot vs. cross

What is the purpose of the dot product as opposed to the purpose of the cross product?

2. ## Re: dot vs. cross

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.

3. ## Re: dot vs. cross

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.