# scalar

1. ### varying vev for a scalar field of complex charge, such as as the Higgs field

Here is some background for my question, which is as I currently understand it (meaning, it may be wrong): In a self-interacting scalar field, the formula for potential energy can be given as (μ^2 * (Φ^2)/2) + (λ * (Φ^4)/4). In a field with an imaginary value for μ, μ^2 becomes negative...
2. ### Why is the product of a scalar and a vector, a vector?

Refer the title.
3. ### How to multiply vector by scalar?

The question is: If (vector d) đ<sub>1</sub> + đ<sub>2</sub> = 5đ<sub>3</sub>, đ<sub>1</sub> - đ<sub>2</sub> = 3đ<sub>3</sub>, 3đ = 2î + 4ĵ, then what are đ<sub>1</sub> and đ<sub>2</sub> in vector notation? I think I have to multiply 5*(2î + 4ĵ), and that will give me đ<sub>1</sub> +...
4. ### vector and scalar?

can i say that all physics definition, which will possibly have both positive and negative values, that the definitions/ quantites can be regarded as a vector? let say if a definition A, whose values can be either +ve or -ve, then it can be regarded as vector?? Thanks!
5. ### Dot and Scalar Products

I have been lost in this forever due to missing the lecture, but does anybody know how to do this? Thank you for the help if you can. a=3.0i+3.0j-2.0k b=-1.0i-4.0j+2.0k c=2.0i+2.0j+1.0k The question is: a(dot)(axb)=?