Coordinates and vectors in space

Coordinates and vectors in space

Build spatial reasoning with coordinates and vectors in three dimensions. This precalculus extension practices coordinate planes, displacement, distance, midpoints, unit vectors and sphere equations. A labeled perspective diagram supports projection reasoning while explicitly warning that a flat sketch does not preserve spatial angles. Single-select and multiselect problems progress from component interpretation to geometric constraints and model checks. Detailed explanations connect every calculation with its meaning and distinguish a vector, a point, a sphere and a plane.