Geometric significance of the dot product
The dot product, or inner product, reads the angle between two vectors, a right angle, and the work of a force.
Dot product and cross product
7 pieces about this concept, across works, topic guides, and exam visualizations.
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Works
Vector projection
Split a vector into a part along a chosen direction and a part at right angles to it, and drag to see the length change with the angle.
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.
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.
Parallelogram area with the edge directions fixed
114 AST Mathematics I, Fill-in 11: the sides stay on two fixed directions, and the area is read from the vector between the center and one vertex.