dot product and cross product

[Disha Karnataki]

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??

 

[albbg]

The cross product of force & displacement gives the torque, that is "how much the force is able to rotate an object around an axis at a certain distance":

https://en.wikipedia.org/wiki/Torque

 

[Ratch]

Disha Karnataki,

if i only have to decide whether the resulting quantity is scalar or vector then what is use of cross or dot product??

You seem to be asking a question such as, "If I need to decide to travel to my destination by water or land, what good is a car or boat?"

Ratch