Well this is the question-

df/dx( 2,-3) = 7 and df/dy (2,-3)=11

i) Find the equation of tangent I get z-f(2,-3)=7(x-2)+11(y+3)

ii) Find the directional derivative Duf(2,-3) in the direction of u=5i-2j

I get 7(5/root29) -11(2/root29) then just simpfly

now my real question is this

Find a non-zero vector v such that Dvf(2,-3)=0

What is the proper working out for this i can just make up any vector provided when I take the gradient vectors dot product i get zero..

can someone show me the proper way ?