What is the magnitude of the electric force on the charge at the bottom left-hand vertex of the triangle due to the other two charges

Explanation:

The magnitude on the charge at the bottom-left corner due to the charge on the top vertex of the triangle will act along the +ve x-axis and the +ve y-axis.

From Coulomb's law the magnitude of the forces on the charge at the bottom-left corner, due to the charge on the top vertex of the triangle are cos 60, and

The magnitude on the charge due to the charge at the bottom-right corner will only act in the -ve x-axis, since they repel each other (like charges repel). The magnitude is  

The angle made by the upper charge to the charge we're considering is 60° with the horizontal.

The total force on the charge along the x-axis is

= cos 60 -

 = -

==> -

For the y-axis, we have

= sin 60

=

The resultant force is

The common factors between the two x-axis force, and the y-axis force is

, we put this outside the square root (squaring this and square rooting will give us the initial value)

=

=  

==>  

the magnitude of the electric force on the charge at the bottom left-hand vertex of the triangle due to the other two charges is

 =  

i believe the answer is a