First of all, I'd like to thank whoever made this website. I sometimes get so stressed with physics & math problems and had no one to ask for help since I'm taking the highest level classes out of all of my friends. I'm so glad I found this website. Here are the problems I need help on: 1) Let r0 = <x0, y0, z0> and r = <x,y,z>. Describe the set of all points (x,y,z) for which a) r dot r0 = 0. b) (r - r0) dot r0 = 0 The 0 next to r, x, y, and z should be subscript. 2) Show that if u and v are vectors in 3-space, then |u x v|^2 = |u|^2 + |v|^2 - (u dot v)^2 (hint: use the pythagorean identity) cos^2 theta + sin^2 theta = 1 3) Show that if u and v are unit vectors and theta is the angle between them, then |u - v| = 2 sin (1/2 theta) Thanks in advance!!!