
Vectors in a Plane and
Space ( Vectors
in 2D and 3D ) 







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 twodimensional system of coordinates), Cartesian
vectors 
Radius vector or position vector 
Vector components 
Vectors in
a twodimensional system examples 
Vectors in
threedimensional 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 threedimensional 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 
Righthanded 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 








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