Discover Questions

Show that the straight lines whose
direction cosines are given by the equations ul+vm+wn = 0 and al2+bm2+cn2 = 0
are
(a) perpendicular? Let X be a set, and let A,B,C⊆X be subsets. Suppose that A∩B= A∩C, and that (X−A)∩B = (X−A)∩C. Prove that B =C? I need help with an algebra question? It's possible to break the 4th dimension? The time? Are black holes essentially gobbling up the universe which would nullify the theory that the universe is expanding?