
Vectors Definition. Main informationPage Navigation:
Vector definitionDefinition. Vector is a directed line segment, ie the segment having a length and a definite direction. Graphically vector depicted as a directed line segments of a certain length. (Fig. 1)
Vector designationThe vector which has a beginning point A and end point B, denoted AB (Fig. 1). Also, the vector represent one small letter, for example a.a. Vector lengthDefinition. The length of the directed segment determines the numerical value of the vector and is called the length of the vector AB.
The length of the vector AB is denoted as: AB. Zero vectorDefinition. Zero vector is a vector whose start and end points coincide.
The zero vector is usually is denoted as 0. The length of the zero vector is zero. Collinear vectorsDefinition. Vector parallel to one line or lying on one line are called collinear vectors (Fig. 2).
Codirected vectorsDefinition. Two collinear vectors a and b are called codirected vectors if their directions are the same: a↑↑b (Fig. 3).
Oppositely directed vectorsDefinition. Two collinear vectors a and b are called oppositely directed vectors if their directions are opposite: a↑↓b (Fig. 4).
Coplanar vectorsDefinition. Vectors parallel to the same plane, or lie on the same plane are called coplanar vectors (Fig. 5).
It is always possible to find a plane parallel to the two random vectors, in that any two vectors are always coplanar. Equal vectorsDefinition. Vectors a and b is an equal vectors if they are in the same or parallel lines, their directions are the same and the lengths are equal (Fig. 6).
Two vectors are equal if they are collinear, codirected and have the same length: a = b, if a↑↑b and a = b. Unit vectorDefinition. Unit vector or orth is a vector whose length is equal to one.
Vectors
Vectors Definition. Main information
Component form of a vector with initial point and terminal point
Length of a vector
Direction cosines of a vector
Equal vectors
Orthogonal vectors
Collinear vectors
Coplanar vectors
Angle between two vectors
Vector projection
Addition and subtraction of vectors
Scalarvector multiplication
Dot product of two vectors
Cross product of two vectors (vector product)
Scalar triple product (mixed product)
Linearly dependent and linearly independent vectors
Decomposition of the vector in the basis
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