Find all real numbers k such that the vectors (1, 2, k) and (2, 4, 3) are distance 3 apart. Let a, b R3. Suppose that for some nonzero v R3, v middot a = v middot b. Is it necessarily the case that a = b? Justify your answer (this means prove the result if it is true, and provide a counterexample if it is false).
