Page 32 - Electrostatics-11

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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 .
Special cases:
⃗⃗
⃗⃗
a) If vectors and are acting along the same direction, = 0°.
2
2
2
= + + 2 0°
2
2
= + + 2
2
2
= ( + )
∴, = +

ℎ ℎ .

0°
−1
, = −1 ( ) = 0 = 0
+ 0°
It means that the resultant vector also moves in the same direction of given
vectors.

⃗⃗
⃗⃗
b) If vectors and are perpendicular to each other, = 90°.
= + + 2 90°
2
2
2
2
= +
2
2
90° . 1
, = −1 ( ) = −1 ( ) = −1 ( )
+ 90° + 0

9 Mechanics