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The formula in the question, \(\vec{F} = q \vec{v} \times \vec{B}\), represents the magnetic force \(\vec{F}\) acting on a charged particle moving in a magnetic field. Here:

- \(q\) is the charge of the particle.
- \(\vec{v}\) is the velocity vector of the particle.
- \(\vec{B}\) is the magnetic field vector.

This formula is a cross-product, which means that the resultant vector \(\vec{F}\) will be perpendicular to both \(\vec{v}\) and \(\vec{B}\) due to the nature of cross products. The correct answer to the question is:

**" \(\vec{F}\) must be perpendicular to both \(\vec{v}\) and \(\vec{B}\)."**

This is because the cross-product \(\vec{v} \times \vec{B}\) inherently yields a vector perpendicular to the plane formed by \(\vec{v}\) and \(\vec{B}\).

Would you like further details on how cross-products work or how magnetic force applies in physics?

### Related Questions
1. What are some real-world applications of magnetic force on moving charges?
2. How does the direction of \(\vec{B}\) affect the direction of the force \(\vec{F}\)?
3. What happens to \(\vec{F}\) if \(\vec{v}\) and \(\vec{B}\) are parallel?
4. How is the magnitude of \(\vec{F}\) calculated in terms of \(\vec{v}\) and \(\vec{B}\)?
5. Why does the cross-product result in a vector perpendicular to both original vectors?

### Tip
To determine the direction of the cross-product \(\vec{v} \times \vec{B}\), use the **right-hand rule**: Point your fingers in the direction of \(\vec{v}\), curl them towards \(\vec{B}\), and your thumb will point in the direction of \(\vec{F}\).

In the formula \(\vec{F} = q \vec{v} \times \vec{B}\), which statement about the directions of \(\vec{F}\), \(\vec{v}\), and \(\vec{B}\) is correct?

Explore the concept of magnetic force acting on a moving charge in a magnetic field with the formula \(\vec{F} = q \vec{v} \times \vec{B}\). Learn how the directions of \(\vec{F}\), \(\vec{v}\), and \(\vec{B}\) relate based on vector cross-product rules. Suitable for high school physics students.

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