$\displaystyle f(x,y,z) = z-x+y$ find $\displaystyle \nabla f(0,0,1)$ plot it on the level surface of f that passes through $\displaystyle (0,0,1)$

$\displaystyle \nabla f = -\hat{i} + \hat{j} + \hat{k} = <-1,1,1>$

$\displaystyle \nabla f (0,0,1) = <-1,1,1>$

and $\displaystyle f(x,y,z)$ is a plane passing through $\displaystyle (0,0,1)$

$\displaystyle z-x+y=1$ find intercepts and draw then plot from (0,0,1) the vector <-1,1,1>

??