Using Jacobian to find tangent plane

132 Views Asked by At

I'm really stuck on this task. I need to find the tangent plane and the normal vector for this set of functions :

x=a cos$\phi$ cos$\psi$,

y=b sin$\phi$ cos$\psi$,

z=c*sin$\psi$

I know the general formula for finding the tangent plane: $z-z_0=z_x'(x-x_0)+z_y'(y-y_0)$ if z=f(x,y) for one function. However, I don't understand the notion of a tangent plane for a set of functions with many variables, similarly presented in the example above. Also, I saw that somehow I can find the Jacobian and hence the partial derivatives of $\phi$ and $\psi$, but still I don't understand how to apply it to the tangent plane formula.