Spatial dot and cross products

Practice spatial dot products and cross products with a focus on meaning, orientation and verification. These precalculus extension questions connect component arithmetic to angles, perpendicular directions, normal vectors and areas. Single-select and multiselect tasks progress from identifying the type of a product to selecting normals, analyzing special cases and diagnosing sign errors. Worked explanations check calculations using independent geometric conditions. A right-handed Cartesian coordinate system is assumed throughout; no calculus is needed.