Exercise 4.1.28

(a) $(1,-1,0)$ is in both planes. Normal vectors are perpendicular, but planes still intersect! Two planes in $R^3$ can’t be orthogonal.

(b) Need three orthogonal vectors to span the whole orthogonal complement in $R^5$.

(c) Lines in $R^3$ can meet at the zero vector without being orthogonal.