Given:
Distance between each electron and proton, r = 1.5 x 10^-10 m
Angle between electrons, θ = 65 degrees

To find:
Magnitude of net electric force exerted on the proton

Solution:
1. Calculate the electric force between the proton and one electron using Coulomb's law:
Fe = (1/4πε0) * (q1*q2)/r^2
where,
ε0 = permittivity of free space = 8.85 x 10^-12 C^2/Nm^2
q1 = charge of proton = +1.6 x 10^-19 C
q2 = charge of electron = -1.6 x 10^-19 C
r = distance between electron and proton = 1.5 x 10^-10 m

Fe = (1/4πε0) * (1.6 x 10^-19 * -1.6 x 10^-19) / (1.5 x 10^-10)^2
Fe = -2.31 x 10^-8 N (force is attractive as proton and electron have opposite charges)

2. Resolve the force Fe into its components along and perpendicular to the line joining the two electrons. Let Fp be the force along the line joining the electrons and Fq be the force perpendicular to it.

Fp = Fe*cosθ
Fp = -2.31 x 10^-8 * cos 65
Fp = -9.45 x 10^-9 N

Fq = Fe*sinθ
Fq = -2.31 x 10^-8 * sin 65
Fq = -1.99 x 10^-8 N

3. The force Fp is balanced by the force of the other electron, since the distance and charge are the same. So, only the force Fq contributes to the net electric force on the proton.

4. The net electric force on the proton is given by the vector sum of Fq and the force due to the other electron, which is equal and opposite to Fq.

5. Magnitude of net electric force on the proton = 2 * |Fq|
|Fq| = 1.99 x 10^-8 N
Magnitude of net electric force on the proton = 2 * 1.99 x 10^-8
Magnitude of net electric force on the proton = 3.98 x 10^-8 N

Final Answer:
Magnitude of net electric force exerted on the proton = 3.98 x 10^-8 N