prove that v is tangent to surface M

[logistic_guy]

here is the question

Prove that: \(\displaystyle \bold{v} = (v_1, v_2, v_3)\) is tangent to \(\displaystyle M: z = f(x,y)\) at a point \(\displaystyle \bold{p}\) of \(\displaystyle M\) if and only if \(\displaystyle v_3 = \frac{\partial f}{\partial x}(p_1,p_2)v_1 + \frac{\partial f}{\partial y}(p_1,p_2)v_2\).

i know the idea but i don't know how to start it because i need three points to take the gradient on that surface \(\displaystyle M\). it give only \(\displaystyle x\) and \(\displaystyle y\). this mean the surface \(\displaystyle M\) is in \(\displaystyle \bold{R}^2\). typo maybe? because i'm expect to take the gradient of \(\displaystyle f(x,y,z)\) not \(\displaystyle f(x,y)\)

 

[blamocur]

i don't know how to start it because i need three points to take the gradient on that surface M.

Why? Do you mean 3 coordinates? -- you have those as (x,y,f(x,y)), don't you?