Page 31 - Electrostatics-11

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3) Null vectors: Vectors having magnitude zero and can take any random

direction is called null vector. The graphical representation of null vector is
⃗
⃗
not possible. It is used to explain the physical phenomenon like − . This
is the physical meaning of null vector. (Note: Isolated existence of null vector
isn’t possible)
4) Opposite vectors: Vectors having same magnitude but opposite direction is
0
called opposite vector. The angle between opposite vector is 180 .
⃗⃗⃗ ⃗⃗⃗

5) Polar vector: Vector which are represent within the same plane are called
polar vector. If the vector is acting in two different planes, then they are

called non-polar vector.

Addition/composition of vectors: The phenomenon of wo or more than two
vectors added to represent single or resultant is called addition of vectors. Vector

quantities are added by the law of vector algebra. It is classified into 3 types.

1. Triangle law

It states that if the two vectors acting on a body be represented by the two sides
of a triangle taken in order then the third side of the triangle taken in opposite
order gives the resultant.

⃗⃗
⃗⃗
Let and be the two vectors acting on a
body making an angle with each other. The
⃗⃗
⃗⃗
vectors and are represented by two sides
AB and BC of the ∆ . The third side AC of
⃗⃗
the triangle gives the resultant .
⃗⃗
⃗⃗
⃗⃗
i.e., = +
Draw CD perpendicular to AB produced in the
figure. From right angle triangle CBD,

= = , =

Also, = = , =

⃗⃗⃗
Magnitude of
2
2
2
From right angled triangle CAD, = +
2
2
= ( + ) +
2
2
= ( + ) + ( )

8 Mechanics