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nobody to answer?
Depends on what you want to exercise.
dot product between vectors v and w ... it provides the angle between the vectors. v.w = | v |. | w |. cos (a)
It is very useful when the vectors are orthogonal ... because the scalar product = 0 v.w
cross product between vectors v and w ... it provides the area of the parallelogram = 2. (area of the triangle)
cross product between vectors u, v and w ... providing the volume of the parallelepiped = 6. (volume of the tetrahedron)
the vector product is useful for calculating areas and volumes.
(I do not know if I understand your question. = /)
Not the answer you are looking for? Search for more explanations.
Cross product: If you have two vectors in 3-space (or n-space), then if you cross those vectors you'll get a vector that is perpendicular. If you have two vectors in 2-space, you'll know if the orthogonal vector goes "in" to the page or sticks "out" of the page depending on which vector your right index finger hits.
Dot product: If you want to find the "projection" of a onto b, then you dot vector a with the unit vector b. You'll get a measurement from the tip of a down to b which forms a right-angle at b.