Question

The point O is the centre of a regular hexagon ABCDEF. Forces of magnitude 7, 3, 10, 9, 6 and 2 newtons act on a particle at O in the directions OA, OB, OC, OD, OE and OF respectively. Find the magnitude of the resultant force and show that it acts in the direction of AC.

Answer 1

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Don't be afraid to draw a diagram according to question's instructions. The diagram will let you put notes and information for your brain to process together.

The force system look like this:


Each of the six forces must now be resolved into the x- and y-components.
x-axis is along OA, y-axis is upwards. OB makes 60 degrees (CCW) with OA, OC 120, OD 180, OE 240 and OF 300 degrees.
This can be done as follows:
The forces are Fa=7, Fb=3, Fc=10, Fd=9, Fe=6, finally Ff=2.
Now make a table and fill it in.
I have done the first and last rows for you.

You will need to compute the table, and the totals (at the bottom).
The totals will be the resultant force, (Fx, Fy).
Since the direction of OC is 120 degrees (CCW) with OA, you need to show that Fy/Fx=tan(120)=1/sqrt(3)=0.577 approx.