Let A be a connected subset of . 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.

b. Prove that there is a point in A whose norm is 4.

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?

b. My question is could I just take the norm of the points u = (0,0,1) and v = (4,3,0) which is and that there must exist a a point whose norm is 4 because it is less than ?

Thank you for your time.