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
         Zero or null vector
      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
         Radius vector or position vector
         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
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