In vector (or multivariable) calculus, we will deal with functions of two or three variables (usually $$x, y$$ or $$x, y, z$$, respectively). The graph of a function of two variables, say, $$z = f(x,y)$$, lies in Euclidean space, which in the Cartesian coordinate system consists of all ordered triples of real numbers $$(a, b, c)$$. Since Euclidean space is 3-dimensional, we denote it by $$\mathbb{R}^{3}$$. The graph of $$f$$ consists of the points $$(x, y, z) = (x, y, f(x, y))$$.