Is the vector field $F=(x+y)\hat i+(1+y^2)\hat j$ perpendicular to the field $G = -(1+y^2)\hat i+(x +y)\hat j$ at every point?

Question

I was tasked with finding a vector field that is perpendicular at every point to the vector field $F = (x+y)\hat i+(1+y^2)\hat j$ .

What I did to get $G = -(1+y^2)\hat i+(x +y)\hat j$ is think of F as a single vector, find a vector that would have a dot product of $0$ with that factor, then let $G$'s equation be that vector I found. I have no clue whether this makes sense.

Any help is appreciated.

Answer 1

HINT

Take the inner product $\langle F,G\rangle$ and see what happens.