The norm of (0, 0, 1) is 1, the norm of (4, 3, 0) is 5. Can you show that "norm" is a continuous function?
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.
For the able part, I got answer to part a), but I am not sure how to solve part b. Can someone help me?
Thanks in advance