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Vector

⚫Introduction
⚪ Those quantities which have both magnitudes and direction are called Vector .
Example : velocity ,accerelation , weight , force are some vector quantities.

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⚫ Representation of vectors :
⚪ Geometrically a vector is represented by a line segment. For example , . Here A is called the initial point and B is terminal point.

Magnitude or modulus of a is expressed as

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⚫ Types of Vector
⚪ Zero vector or null vector : A vector whose magnitude is zero is called zero or null vector.
⚪ Unit Vector : A vector whose magnitude is unity (1). The unit vector in the direction of a vector a is denoted by .

⚪ Collinear or Parallel Vector : Vectors having the same or parallel supports are called collinear or parallel vectors
⚪ Co-initial Vector : Vectors having the same initial point.
⚪ Coplanar Vector : A system of vectors is said to be coplanar, if their support are parallel to the same plane.
⚪ Coterminous Vectors : Vectors having the same terminal point.
⚪ Equality of Vectors : Two vectors a and b are said to be equal if
       i) |a|= |b|
       ii) They have the same or parallel support

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⚫ Addition Of Vectors
⚪ Triangle Law of addition :

If in Δ ABC
AB = a , BC = b , AC = c , then AB + BC = AC i.e., a + b = c
⚪ Parallelogram law of addition :

If in a parallelogram OACB , OA = a , OB = b , OC = c , Then OA + OB = OC , it means a + b = c , where OC is the diagonal of the parallelogram OABC
⚪ Addition in component Form :
If the vectors are defined in terms of i , j and k. It means if
a = a₁i + a₂j + a₃k
b = b₁i + b₂j + b₃k
Their sum is defined as :
a + b = (a₁ + b₁ )i + (a₂ + b₂ )j + (a₃ + b₃ )k

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Lecture 13

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Practice set 1 Practice set 2 Practice set 3