Algebraically prove that if a = perp ;, then perpa (v) = proj. Then, draw a diagram and give a one sentence explanation of why this makes sense geometrically. You can derive the formula for proj v using three observations: proj = cw for some c R v=proj + perp v perp is orthogonal to w . Show that c= using the dot product and the observations above. Prove that there are exactly 6 unit vectors with integer components in R orthogonal to e1. What special notation do we have for these vectors? v. If u and v are nonzero vectors such that proj(u) = and proj() = -, find the angle between u and