# The direction Of three forces 1N,2N,3N are acting at a point are parallel to the sides of an equilateral Triangle taken in order. The magnitude of their resultant??

1
by syke

2016-05-03T21:13:16+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
The three forces will be along three directions separated by 120 deg. from each other drawn at a point P.  Let them be  PA of 1 N.  PB = 2 N  and then  PC = 3 N..

Let us draw PA  horizontally along  positive x axis.
PB is at 30 deg. anticlockwise from + y axis.
PC will be at   30 deg. clockwise from  - y axis...

Resolving components along x axis and adding:
= 1 N +  2 N * Cos 120 + 3 N * Cos 240
=  1 - 2 * 1/2 - 3 /2  =  - 3/2 Newtons

Resolving components along y axis and adding
= 0 N + 2 N * √3 /2  -  3 N * √3/2   =  - √3/2  Newtons

So resultant is    R =  -1.5 i  - √3 /2  j  where   i and j  are unit vectors.
magnitude =     √[ 1.5² + 3/4 ]   = √3  Newtons.

======
The calculations are much simpler,  if you take  2 Newtons force/vector along x axis and the other two at 120 deg. on either side to that....