Introduction to Vectors

  • A quantity that has both magnitude and direction is called a vector quantity.
  • A quantity that has magnitude only is called a scalar quantity.
  • A line segment that has a particular direction is called a directed line segment.
  • Every directed line segment is associated with length, support and sense.
  • The distance between the initial point and terminal point is called the length (or magnitude) of the vector. The length of a directed line segment is denoted by its modulus. The straight line of an unlimited length of which a directed line segment is a part is called its line of support or simply the support. Two directed line segments having the same or parallel support may have the same or opposite sense.
  • Directed line segments will be considered equivalent, if and only if, they lie on the same or parallel support and have the same length and same sense of direction.
  • The length of the line segment is proportional to the magnitude of the vector. The direction of the line segment is the direction of the vector.
  • The distance between the initial point and terminal point is called the length (or magnitude) of the vector.
  • In mathematics, a quantity which describes a change in position is called a displacement vector.
  • A vector whose initial and terminal points are coincident is called the zero or null vector.
  • Three or more vectors, which neither lie in the same plane nor are parallel to the same plane, are called non-coplanar vectors.
  • Vectors having same or parallel support irrespective of their magnitude and direction are called collinear vectors.
  • Vectors having the same initial point are called co-initial vectors.
  • Vectors having same magnitude and direction, regardless the positions of their initial points are said to be equal.
  • A vector that has the same magnitude as the given vector but the opposite direction is called the negative of the given vector.
  • Two vectors are said to be like vectors if they have the same direction and are said to be unlike vectors if they have the opposite directions.
  • A vector is said to be free or non-localised vector if its origin can be taken anywhere in space.
  • Three or more vectors that lie in the same plane or are parallel to the same plane are called coplanar vectors.

Keywords: Notation for a vector, Position vector, proper vectors, localized vectors, reciprocal vectors, non-collinear vectors, unit vectors, non-coplanar unit vectors, free vectors, direction cosines and direction ratios of a vector

 

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  • Q5

    Define non-coplanar vectors.

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    Three or more vectors, which neither lie in the same plane nor are parallel to the same plane are called
    non-coplanar vectors.

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