MathFormaVector Algebra
Study vectors given by their coordinates in space, including linear operations, length and direction, and the three products (scalar, vector, and mixed) used to find angles, areas, volumes, and normals.
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BASIC DEFINITIONS
Basic Definitions
The core operations on vectors given by coordinates — sums and length, the scalar, vector and mixed products, and projection onto an axis — the tools used throughout the problems below.
1Problem 1 · Angle Between an Edge and a Space DiagonalUse the scalar product to find the angle between edge A′D′ and space diagonal DB′.Start →2Problem 2 · Area of a Triangular SectionUse the vector product to find the area of the section EB′C.3Problem 3 · Volume of a TetrahedronUse the mixed product to find the volume of the tetrahedron EB′C′C.4Problem 4 · Unit Normal to a PlaneUse the vector product to find the two unit vectors perpendicular to the plane B′CE.5Problem 5 · Foot of a PerpendicularUse the projection of a vector to find the foot of the perpendicular from A′ onto line AB.