Two forces `F and 2 F` newton act on a particle. If the first force be doubled and the second force be increased by `16 ` newtons, the direction of the resultant remains unaltered. Find the value of `F`.

Explanation

To solve the problem, we need to analyze the forces acting on the particle and how they change when we modify their magnitudes. Let's break down the solution step by step.

### Step 1: Define the Forces
Let the two forces acting on the particle be:
- \( F_1 = F \)
- \( F_2 = 2F \)

### Step 2: Resultant of Initial Forces
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