the dot product of two vectors is scalar.
cross product of two vectors is vector.
my question is:i know that force is vector so as displacement but the dot product of force & displacement gives scalar i.e is nothing but work done.
i know already that work-done is a scalar quantity but, if i didn't knew that it is a scalar then suppose i go to take a cross product of these two vectors then i will get a vector out of it which is directed perpendicular to the surface of these to vectors acting.what will i name this new vector or rather what is it??
now,if i only have to decide whether the resulting quantity is scalar or vector then what is use of cross or dot product??