Rotating Electric Forces: How to Find X Values to Change Net Force Direction?

[jfsbird]

Homework Statement

Particles 2 and 4, of charge -e, are fixed in place on the y-axis at y2=-10.00 cm and y4=5.00cm. Particles 1 and 3, of charge -e, can be moved along the x axis. Particle 5 of charge +e is fixed at the origin. Initially particle 1 is at x1= -10.0cm and particle 3 is at x3= 10.0cm. (a) to what x value must particle 1 be moved to rotate the direction of the net electric force Fnet on particle 5 by 30 degrees counterclockwise? (b) With particle 1 fixed at the new position, to what x value must you move particle 3 to rotate Fnet back to its original position?

Homework Equations

F=k*qq/r^2

The Attempt at a Solution

I have found the individual forces and the net force in vector notation, but can't seem to see the way to handle the rotation. I knowwhat the correct answer is but not how to get there.

 

[Shooting Star]

If a 2-d vector xi + yj is rotated by an angle ‘b’ in the counter clockwise direction keeping the magnitude constant, then the new vector is given by:

(xcos b - ysin b)i + (xsin b + ycos b)j.

This should solve your problem.