A charge Q located at a point `vec r` is in equilibrium under the combined field of three charges `q_(1), q_(2)` and `q_(3)`. If the charges `q_(1)` and `q_(2)` are located at point `vec r_(1)` and `vec r_(2)` respectively, find the direction of the force on Q due to `q_(3)` in terms of `q_(1),(q_2), vec r_(1) vec r_(2)`, and `vec(r)`.

Explanation

To solve the problem, we need to analyze the forces acting on the charge \( Q \) due to the other three charges \( q_1, q_2, \) and \( q_3 \). Since the charge \( Q \) is in equilibrium, the net force acting on it must be zero. Let's break down the solution step by step.

### Step 1: Understand the Forces Acting on Charge \( Q \)

The charge \( Q \) experiences forces due to charges \( q_1 \), \( q_2 \), and \( q_3 \). We denote the forces as follows:
- \( \vec{F}_1 \): Force on \( Q \) due to \( q_1 \)
- \( \vec{F}_2 \): Force on \( Q \) due to \( q_2 \)
- \( \vec{F}_3 \): Force on \( Q \) due to \( q_3 \)
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