Vector : A vector is a quantity which has magnitude and is also related to a definite direction. Where as in a scalar quantity which has magnitude but does not passess direction.
Thus, mass, density, volume, temperature, distance, speed, heat, time, etc are scalar quantities, whereas displacement, velocity, acceleration, force and the intensity of an electric field etc are vector quantities.
Types of Vectors
- Like and Unlike Vectors : The two vectors of same direction are called like vectors. The vectors having opposite line of action are called unlike vectors.
- Equal Vectors : If magnitude and direction of two vectors are same, then those are called equal vectors.
- Zero (Null) Vector : A vector whose magnitude is zero is called zero vector.
- Unit Vector : A vector whose modulus is unity, is known as unit vector. Unit vector of â is denoted by â and â = a/|a|
- Collinear Vectors : Two or more vectors are known as collinear vectors, if they are parallel to a given straight line. The magnitude of collinear vectors can be different.
- Coplanar Vectors : Those vectors which are parallel to the same plane are called coplanar vectors.
- Position Vector : If O is a fixed point in a space, then vector OP which represents the position of a point P, is known as position vector of P.
- Displacement Vectors : If a particle is displaced from A to B, then displacement AB is a vector and AB is called the displacement vector of that particle.
AB=OB-AB
- Linearly Independent Vectors : A set of vectors a₁, 82,..., an is said to be linearly independent, if x₁a₁ + x₂a₂ +...+ xnan = 0 = xn ⇒ x1=x2=.....=xn=0
- Linearly Dependent Vectors : A set of vectors a₁, a2, ..., an is said to be linearly dependent, if there exists scalars x₁, x2, ..., xn not all zero such that
x1a1+x2a2+.....+xnan = 0
