VECTOR

There are two types of physical quantities.

Scalars:

Those physical quantities which possess only magnitude and no direction are called scalars.

  • It is specified completely by a single number, along with the proper unit.
  • Scalars can be added, subtracted, multiplied and divided just as the ordinary numbers i.e by using the rules of ordinary algebra.
  • Some examples of vectors are mass, time, distance, speed, work, energy, power etc.

Vectors:

Those physical quantities which possess both magnitude and direction are called vectors.

  1. A vector is specified by giving its magnitude (a number along with its unit) and its direction.
  2. Some examples of vectors are displacement, velocity, acceleration momentum, force etc.
  3. Vectors can’t be added, subtracted, multiplied and divided just as the ordinary numbers i.e by using the rules of ordinary algebra.
  4. Vectors are added by using by using ‘Triangle Law of addition’ or by ‘parallelogram law of addition’.
  5. Some of the quantities, like current, are having both magnitude and direction but are not considered vector quantities, because they do not follow laws of addition.

 ‘A vector quantity is a quantity that has both a magnitude and a direction and obeys the triangle law of addition or equivalently the parallelogram law of addition’.

Vectors and Scalars

( In Hindi + English Mix)

Types of Vector:

.

  1. Equal vectors: Two vectors having same magnitude as well as direction are known as equal vectors.

  1. Negative or Opposite vectors: A vector having same magnitude as that of a given vector and the direction opposite to the given vector is called the negative or opposite vector to the given vector.

  1. Collinear vectors: All those vectors which either act along the same line or act along parallel lines are called collinear vector.

 

  1. Co initial vectors: All those vectors which start from the same point are known as co-initial vectors.

  1. Co-terminus vector: All those vectors which terminate at the same point are known as co-terminus vector.

  1. Co planar vector: All those vectors which act along the same plane are called co planar vector.

Unit Vectors:

Unit vector along a given vector is a vector of unit magnitude and has the same direction as that of the given vector.

It is mathematically defined as

                                                ……….. (i)

 

                                         ………… (ii)

  • Physically, unit vector represents the direction of the given vector.
  • The unit vectors which are mutually perpendicular to each other are known as orthogonal unit vectors.

Position Vector:

 

A vector representing the position of a point in space with respect to the origin of a co-ordinate system is known as position vector of the point.

The position vector of point P (x, y, z) is given by

= x (along x axis) + y (along y axis) + z (along z axis)

or,      ….…. (i)

Magnitude of the position vector is given by           ………. (ii)

Unit vector along the given vector ()                   

                                          

                                                                   …. (iii)

Displacement Vector

Let a particle is initially present at point P (x1, y1, z1) and it moves to another point Q (x2, y2, z2) then the position vector of initial and final position are

      ………. (i)

       ……… (ii)

Then the displacement vector is given by

       

 

Or            …………. (iii)

So magnitude of the displacement vector is  

    …………. (iv)

Question1.       A particle initially present at point (1m, 2m, 1m) moves to another point (3m, -1m, 2m) in 2 sec.  Determine its average velocity.

Solution.          (1m, 2m, 1m) = (x1, y1, z1)

                            (3m, -1m, 2m) = (x2, y2, z2)

                  

  Or      

 Or       

              

                                 

      Or                       

Magnitude of the average velocity is     

        

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