# Can anyone describe to me the difference between dot product and cross product?

1. Oct 15, 2008

I guess one of them is scalor and one of them is vector, but what is the REAL DIFFERENCE between them?

gracias

2. Oct 15, 2008

### BoundByAxioms

Well, like you said, the dot product gives you a scalar and the cross product gives you a vector.

Also, cos$$\theta$$=$$\frac{x \cdot y}{||x||||y||}$$ whereas
a x b = (||a||)(||b||)sin$$\theta$$(n), where n is the unit vector perpendicular to the plane containing a and b.

The dot product essentially gets you a scalar from two vectors, which is directly related to the formula for the dot product. If you want to learn more, read a linear algebra text. A cross product gets you a vector that is perpendicular to both a and b (provided that a and b are not colinear, in which case the result will be the zero vector).

3. Oct 15, 2008

thanks!

4. Oct 15, 2008

### Staff: Mentor

There are a lot of differences between them. The cross product can be thought of as a map from R^3 x R^3 to R^3. In other words it takes as input two 3-D vectors, does something to them that produces a third vector in R^3 that happens to be orthogonal to both of the input vectors. The cross product is defined only for 3-D vectors.

The dot product is much more general, and is one example of an operation called an inner product. A vector space with the additional structure of an inner product is called an inner product space. The dot product you're probably familiar makes R^2 and R^3 (and R^n) inner product spaces. Besides vector spaces, function spaces can have inner products defined for them, and they can be defined in a variety of ways: as a sum or an integral or as a product of matrix multiplication. In all cases the inner product results in a number, so can be thought of as a mapping from V x V to a field such as R.

If you search Wikipedia using "inner product" or "dot product" or "inner product" you'll find a lot more information.
Mark