Help with Electric Forces Problem and Equilateral Triangles

[Phy_TR]

Homework Statement

The point charges in the figure have the following values: q1=+2.1μC, q2=+6.3μC, q3=−0.89μC. Suppose that the magnitude of the net electrostatic force exerted on the point charge q2 in the figure is 0.57 N .
Find the distance d and the direction (angle) of the net force.

Homework Equations

(I think) F=k|q||q|/d^2
and pythagorean theorem

The Attempt at a Solution

I really think I overcomplicated myself in the beginning (I separated each F12 and F23 into its x and y components), but my most recent solution goes:
F12 = k|q1||q2|/d^2
F23 = k|q2||q3|/d^2

and then attempting to do (0.57)^2 = (k|q1||q2|/d^2)^2+(k|q2||q3|/d^2)^2
and solving for d. I know the right answer is 0.43 m but I truly don't know how that is (neither of my two methods have worked). I've been doing this for two hours (to my embarrassment) so any input would be very much appreciated.

Thanks in advance.
(Also, is responding to these three questions what using the template means?)

 

[TSny]

The Attempt at a Solution

I really think I overcomplicated myself in the beginning (I separated each F12 and F23 into its x and y components),

Yes, that's the way to approach it. If you show us some details of what you did, maybe we can spot the error.

but my most recent solution goes:
F12 = k|q1||q2|/d^2
F23 = k|q2||q3|/d^2

and then attempting to do (0.57)^2 = (k|q1||q2|/d^2)^2+(k|q2||q3|/d^2)^2
and solving for d.

This won't work because the forces F₂₁ and F₂₃ are not perpendicular to one another.

(Also, is responding to these three questions what using the template means?)

Using the template just means filling in all three parts of

Homework Statement

Homework Equations

The Attempt at a Solution

You did that very nicely!

 

[Phy_TR]

You did that very nicely!

Awesome, thanks!

Ok, so this is what I did when I decomposed the vectors the first time:

F_12x= cos60F₁₂
F_12y= sin60F₁₂

and

F_23x= F₂₃
F_23y= 0

giving me:

F_NetX = F_23X-F_12X (because they're going opposite I used the negative sign)
F_NetY = F_12Y

And then I did the pythagorean theorem for all of that:
(F_23X-F_12X)²+(F_12Y)²=F_Net²

[(k|q2||q3|/d^2 - cos60(k|q1||q2|/d^2)]² + [sin60(k|q1||q2|/d^2)]² = F_Net²

...and it works now...
I wish I hadn't erased my first attempt (then I would've know what went wrong), but surely it was the part with the F_NetX because I don't remember getting a negative answer to that before...wow.

This won't work because the forces F21 and F23 are not perpendicular to one another.

Yes *facepalm*, it seems silly to have given up on my previous plan for that one!

Thank you so much TSny, and sorry about that!

 

[TSny]

Ok, so this is what I did when I decomposed the vectors the first time:

F_12x= cos60F₁₂
F_12y= sin60F₁₂

Good. (I'm assuming you're taking the x-axis to be horizontal and the y-axis vertical.)

F_23x= F₂₃
F_23y= 0

This doesn't look right. F₂₃ does not point along the x axis.

Just to make sure we're together, can you describe in words the directions of F₁₂ and F₂₃ acting on q₂?