in what direction?

given that the equation of a mountain is z = sin (xy) +exp (y). in which direction should john walk at the location (2,0,1) if he wants to stay at the same elevation?


my working,
i found out that grad f at (2,0,1) is (0,3) and i know that grad f is perpendicular to the lever curve...but how do i solve this?



thanks..

He can walk in any direction perpendicular to the gradient. The gradient has a zero x-component, and thus any vector with a zero y-component is perpendicular to the gradient as the dot product between the two vectors is zero. That is, he should walk along a line parallel to the x-axis.