Calculate the magnitude and direction of the Coulomb force on each of the three charges connected in series:

1st - 6 micro Coulombs (positive charge)
2nd - 1.5 micro Coulombs (positive charge)
3dr - 2 micro Coulombs (negative charge)
Distance between 1st and 2nd - 3cm
Distance between 2nd and 3rd - 2cm

To calculate the magnitude and direction of the Coulomb force on each of the three charges, we can use the formula for the Coulomb force:

F = k * (q1 * q2) / r^2

where F is the Coulomb force, k is the Coulomb's constant (approximately 9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

First, let's calculate the force between the first and second charges:

Magnitude:
F12 = k * (q1 * q2) / r^2

= (9 × 10^9 N m^2/C^2) * (6 × 10^-6 C) * (1.5 × 10^-6 C) / (0.03 m)^2

= 1.8 × 10^-3 N

Direction:
Since both charges are positive, the force between them will be repulsive. Therefore, the direction of the force is away from each charge.

Now, let's calculate the force between the second and third charges:

Magnitude:
F23 = k * (q2 * q3) / r^2

= (9 × 10^9 N m^2/C^2) * (1.5 × 10^-6 C) * (-2 × 10^-6 C) / (0.02 m)^2

= -67.5 × 10^-3 N

Direction:
Since one charge is positive and the other is negative, the force between them will be attractive. Therefore, the direction of the force is towards the charges.

Finally, the force acting on the first charge due to the second and third charges will be equal in magnitude but opposite in direction to the forces we calculated above:

Magnitude:
|F21| = |F12|

= 1.8 × 10^-3 N

Direction:
The direction of the force on the first charge will be opposite to the direction of F12, which is towards the second charge. So, the force on the first charge will be towards the third charge.

In summary, the magnitudes and directions of the Coulomb forces are:

1st - 6 micro Coulombs (positive charge):
Magnitude: 1.8 × 10^-3 N
Direction: Towards the third charge

2nd - 1.5 micro Coulombs (positive charge):
Magnitude: 1.8 × 10^-3 N
Direction: Away from both charges

3rd - 2 micro Coulombs (negative charge):
Magnitude: 67.5 × 10^-3 N
Direction: Towards the second charge