New solution based on geometric interpretation of projection

According to the lecture note,

http://www.math.ubc.ca/~elyse/152/2018/7TransformationsRandomWalks.pdf

I think students also understand geometric picture of the projection operator. Actually, if you think this problems geometrically, it is easier to get the solution because you don't need to compute the projection matrix. So it would be great if anyone add a new solution based on this.