Problem $2.$ Our course has looked at projections recently. You read about it in the reading and some of the instructors have described the projection of an object as its $$shadow$$ at noon. The idea is that when $$a$$ we look at a point with position vector $$b$$ above a horizontal ground $($z $=0),$ with the sun directly above c us$,$ the shadow that is cast is created by taking the vertical line through that point, $$y$=$b$+$ t $0,$a$$ and finding its intersection with the ground. This gives us the $$shadow$-$ or projection $-$ of $$b$.$ We c then generalize the idea for any line and a plane that is orthogonal to it$,$ and goes through the origin. Notice that the readings refer to these maps as orthogonal projections. That name is given because the line along which we imagine the rays of the sun is orthogonal to the plane we are taking as the ground. We could, however, create other projections by having the line meet the plane at any angle. Take any plane P through the origin and a line l$,$ also through