Spatial vectors, planes, and lines
Fix one vector and one plane, and answer in order where it is, which way the plane faces, and how the two are related.
Spatial vectors
7 pieces about this concept, across works, topic guides, and exam visualizations.
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Topics
Works
Geometric significance of the cross product
Change the angle, length, and tilt of two spatial vectors and read the parallelogram area, the normal n, and the angle together.
Spatial vector and three plane projections
Drag the components and watch the projections on the xy, xz, and yz planes describe one vector in space.
Where a line meets a plane
Drag the start and direction of a line, and the normal and constant of a plane, and watch an intersection, a parallel line, or a line lying in the plane.
Plane normal and distance from a point
Drag the normal n and a point fixed on the plane, and read ax+by+cz=h together with the distance from a point to the plane.
Exam visualizations
Skew lines, the common perpendicular, and distance in space
112 GSAT Mathematics A, Fill-in 17: use direction vectors and the common perpendicular to combine three mutually perpendicular lengths into a distance in space.
Distance between parallel traces of a plane on the coordinate planes
114 AST Mathematics I, Fill-in 10: a plane meets two coordinate planes in parallel lines; find the shortest distance between them.