A rectangular plate with sides $~a~$ and $~b~$ is subjected to a pressure force. The pressure(force per unit area) at any point on the plate is proportional to the square of the distance of that point from one corner. Find the total force on the plate.
I was looking at the formula $~F=PA~$, where $~P~$ will be $~k(x^2+y^2)~$ and $~A=dxdy~$.
After using double integrals $$~\int_0^a\int_0^b k(x^2+y^2)dxdy~.$$ I get a solution in the from of $~k(ab/3)(a^2+b^2)~$.
What has me confused is that I thought force was supposed to be a vector but it appears to be that I have gotten a scalar value.
I am studying a mathematics course so some physics is lost on me. Any help would be appreciated.
Cheers,