Difference between dot and cross product

If you have two vectors A and B,
Dot product is a scalar quantity dealing with how much of one vector is in the same direction as the other vector, or the projection of one onto the other. You can see that from the cosine part of this form-


The cross product is a vector perpendicular to both A and B. It deals with how much of one vector is perpendicular to the other vector. You can see that in the sine part of this form -