Final answer:
The magnitude of the resulting vector R is 7.2 N and the direction is 45 degrees from the positive x-axis.
Step-by-step explanation:
To find the magnitude and direction of the resulting vector R, we can use the principle of superposition. The principle states that the total force on a charge due to multiple charges is the vector sum of the individual forces. In this case, we have three charges: q1, q2, and q3. To find the magnitude of R, we can use the formula F = k * |q1 * q3| / d13^2, where k is the Coulomb's constant and d13 is the distance between q1 and q3.
Substituting the given values, we have F = (9 * 10^9 N*m^2/C^2) * (2 * 10^-6 C * 4 * 10^-6 C) / (0.5 m)^2 = 7.2 N (rounded to the nearest tenth). To find the direction of R, we can use the concept of electric field. The electric field due to q1 and q2 will be in the positive x-direction, while the electric field due to q3 will be in the positive y-direction. Hence, the resulting vector R will be in the positive x-y plane, making an angle of 45 degrees with the positive x-axis.