A charge q equals to 3.4c is located at x equal 2m and y equal 2m and a second charge q2 equal to 2.7c is located at x equal 4m and y equal -4m..where must a third charge q be placed such that the resolutant force on it is zero .

To find the position where a third charge q must be placed such that the resultant force on it is zero, we need to consider the forces exerted by the first two charges.

The force between two charges can be calculated using Coulomb's Law:

F = k * |q1 * q2| / r^2

where F is the force between the charges, k is the electrostatic constant (k = 9 * 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

First, let's calculate the force exerted by charge q1 on charge q:

F1 = k * |q * q1| / r1^2

where r1 is the distance between charge q1 (2 m, 2 m) and the point where we want to place charge q.

Similarly, let's calculate the force exerted by charge q2 on charge q:

F2 = k * |q * q2| / r2^2

where r2 is the distance between charge q2 (4 m, -4 m) and the point where we want to place charge q.

To have a net force of zero on charge q, the magnitudes and directions of F1 and F2 should cancel each other out. The magnitudes of the forces depend on the charges and the distances between them, while the directions depend on the signs of the charges.

Let's assume the charge q is positive (q > 0). If we place charge q symmetrically between q1 and q2, the forces will have opposite directions and cancel each other out. Since the charges q1 and q2 have opposite signs (q1 is positive and q2 is negative), we can conclude that the third charge q should be placed at the midpoint between (2 m, 2 m) and (4 m, -4 m).

Using the midpoint formula, the x-coordinate of the midpoint is: (2 m + 4 m) / 2 = 3 m

Similarly, the y-coordinate of the midpoint is: (2 m + (-4 m)) / 2 = -1 m

So, the third charge q should be placed at (3 m, -1 m) in order to have a resultant force of zero.