Pre-calculus Contents I

 Vectors in a Plane and  Space
Vectors in a Plane Vectors - introduction
Length, magnitude or norm of the vector Collinear, opposite and coplanar vectors Addition of vectors
Triangle rule (law) and parallelogram rule Subtraction of vectors Scalar multiplication or multiplication of a vector by scalar
Unit vector Addition, subtraction and scalar multiplication of vectors, examples Linear combination of vectors Linear dependence of vectors Vectors and a coordinate system, Cartesian vectors Vectors in a coordinate plane (a two-dimensional system of coordinates), Cartesian vectors
Vector components
Vectors in a two-dimensional system examples Vectors in three-dimensional space in terms of Cartesian coordinates
Angles of vectors in relation to coordinate axes, directional cosines - scalar components of a vector
The unit vector of a vector
Vectors in a three-dimensional coordinate system examples Scalar product or dot product or inner product
Orthogonality or perpendicularity of two vectors
Different positions of two vectors and the corresponding values of the scalar product
Square of magnitude of a vector Scalar product of unit vectors
Scalar or dot product properties Scalar product in the coordinate system
Angle between vectors in a coordinate plane Projection of a vector in the direction of another vector, the scalar and vector components Vector product or cross product Vector product
Right-handed system
An example for the vector product in physics
The condition for two vectors to be parallel
The vector products of the standard unit vectors
The vector product properties
The vector product in the component form The mixed product or the scalar triple product
The mixed product or scalar triple product definition
The mixed product properties
The condition for three vectors to be coplanar
The mixed product or scalar triple product expressed in terms of components The vector product and the mixed product use, examples   Pre-calculus Contents 