Question 5
Let $ABCDEFGH$ be a cube. A plane $P$ passes through $A$ and makes equal angles with the three edges $AB,AD,AE$.
(a) Find the common cosine of these three equal angles and construct the orthogonal projection of the cube onto $P$.
(b) Use this projection to discover as many noteworthy relations as possible between $P$ and the lines joining pairs of the eight vertices, and the planes containing triples of those vertices.
(a) Find the common cosine of these three equal angles and construct the orthogonal projection of the cube onto $P$.
(b) Use this projection to discover as many noteworthy relations as possible between $P$ and the lines joining pairs of the eight vertices, and the planes containing triples of those vertices.