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The problem you’ve provided involves the composition of multiple force vectors, with the goal of finding the resultant vector both graphically and analytically.

Here is the setup as described in the image:

1. **Vector \( \vec{V_1} \)** has a magnitude of 70 kgf and is at 0° (along the positive x-axis).
2. **Vector \( \vec{V_2} \)** has a magnitude of 100 kgf and is at an angle of 30° from the positive x-axis.
3. **Vector \( \vec{V_3} \)** has a magnitude of 90 kgf and is at an angle of 45° from the positive y-axis.
4. **Vector \( \vec{V_4} \)** has a magnitude of 70 kgf and is at an angle of 180° (along the negative x-axis).

We can solve this analytically using vector decomposition into their components.

### Step 1: Break each vector into x and y components
We use the formulas:
- \( V_x = V \cos(\theta) \)
- \( V_y = V \sin(\theta) \)

For each vector:
1. **\( \vec{V_1} \) (70 kgf at 0°):**
  

Resuelve esto por favor: Los siguientes vectores actúan todos sobre un mismo punto. Hallar gráficamente y analíticamente su resultante y su dirección. V1 = 70 kgf, V2 = 100 kgf (30°), V3 = 90 kgf (45°), V4 = 70 kgf (180°).

Learn how to calculate the resultant of four force vectors acting on a single point, with magnitudes and angles provided. This problem involves vector decomposition, trigonometry, and the Pythagorean theorem to find the resultant vector and its direction. Suitable for students in Grades 10-12.

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