Stage 29 · Spatial Vectors & Solid Geometry
29.3.6 Combined Proofs of Parallel and Perpendicular
29.3 Seeing Parallel and Perpendicular with Vectors — Direction and Normal Vectors
Point 6 of 6
29.3.6 Combined Proofs of Parallel and Perpendicular
Core ideaSwap every tricky picture problem for the question of whether dot products of d and n are zero, and the proof becomes plain arithmetic.
Module goal. Translate lines and planes into two handy "keys," the direction vector and the normal vector, and use vectors being collinear or perpendicular to settle parallelism and perpendicularity among lines and planes.