Let A be a connected subset of $\displaystyle R^3$. Suppose that the points (0,0,1) and (4,3,0) are in A.

a. Prove that there is a point in A whose second component is 2. (...)

a. Let u = (0,0,1) v = (4,3,0) be points in A. Next, I find the symmetric equation of the line l that contains the points u,v.

Thus,

.

We use the first point u to find the symmetric equation of l.

Thus, the equation yields:

It is sufficient to show that there exists a y such that y/3 = 2 that disconnects A into two disjoint sets?