What is the difference between dot and cross products in vector operations?

[FUNKER]

i was taught in my physics lecture that Work =Force *distance *cos(A)
to my belief this is the dot produict and used to measure area.
in my maths lecture two vectors using the cross product is also used to find the area ie: N x M = N*M*sin(A)
i thought that one product was used for area and the other for a different use along the lines of the projection of one vector upon another?
help

 

[Chen]

i was taught in my physics lecture that Work =Force *distance *cos(A)
to my belief this is the dot produict and used to measure area.

You are correct that this is the dot product, but it is not used to measure area. The geometric meaning of the product of X-dot-Y is the length of the projection of vector X on the vector Y. Try drawing it for a better understanding.

in my maths lecture two vectors using the cross product is also used to find the area ie: N x M = N*M*sin(A)
i thought that one product was used for area and the other for a different use along the lines of the projection of one vector upon another?

I don't know the geometric meaning of the cross product, but one property is that the resulting vector is always perpendicular to both original vectors. So for example, when dealing with surfaces you can find the normal vector by cross-product-ing two independent vectors on the surface itself.

 

[cookiemonster]

The dot product is not used to find area. As Chen said, it is the length of the projection.

The magnitude of the cross product is the area of a parallelogram described by the two vectors.

cookiemonster