Page 34 - Electrostatics-11
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= = , =
Also,
= = , =
⃗⃗⃗
Magnitude of
2
2
2
From right angle triangle CAD, = +
2
2
= ( + ) +
2
2
= ( + ) + ( )
= + 2 + +
2
2
2
2
2
2
2
2
2
= + 2 + ( + )
2
2
2
= + 2 +
= √ + + 2
2
2
⃗⃗
It gives the magnitude of resultant .
⃗⃗⃗
Direction of
⃗⃗
⃗⃗
Let β be the angle made by the resultant with
Now, from triangle CAD,
= = =
+ +
= −1 ( )
+
⃗⃗
It gives the direction of resultant .
3. Polygon law: If the number of different vectors acting on a
particle simultaneously represent the many sides of a ⃗
polygon in terms of both magnitude and direction, then the
⃗
closing line taken in opposite order will be their resultant.
⃗⃗
⃗
⃗⃗
Mathematically, = + + ⃗ + + ⃗ ⃗
⃗
⃗
Resolution of Vector: The process of splitting of a vector into number of its
components in specified direction is called resolution of vector. It is exactly
opposite phenomenon of composition of vectors.
11 Mechanics
