About vectors and vector products

[kapoor_kapoor]

If two physical quantities are being multiplied , is there any way to know that the result will be a scalar of vector.. Moreover if two vectors are being multiplied how can we know that we have to apply cross or dot product??

 

[DEvens]

You need some context. "Two physical quantities" is too vague for it to be possible to know what is going on. Physical quantities can be many different forms. Temperature would presumably be a scalar. The velocity field of a fluid would be a vector field. The stress in a solid is probably expressed as a tensor. And so on.

"Being multiplied" is likewise too vague to understand what is going on. For example, some quantities are a scalar times a scalar in some contexts. In other contexts they might be a scalar times a vector. Or a cross product. Or a dot product.

 

[mathman]

Dot product and cross product are mathematically defined vector operations, resulting in a scalar or a vector respectively. Physics gives particular meaning to the results.

 

[BobG]

If two physical quantities are being multiplied , is there any way to know that the result will be a scalar of vector.. Moreover if two vectors are being multiplied how can we know that we have to apply cross or dot product??

A dot product will get you the angle between two vectors.

A cross product will get you a new vector that presumably represents some physical property (angular momentum, torque, etc). Geometrically, the magnitude of the cross product gives you the area of a parallelogram whose sides are defined by the two vectors you took the cross product of.