The force `vecF` experienced by a particle of charge q moving with a velocity `vecv` in a magnetic field `vecB` is given by `vecF=q(vecvxxvecB)`. Which pairs of vectors are at right angles to each other?

Options

A. `vecF` and `vecv`
B. `vecF` and `vecB`
C. `vecB and vecv`
D. `vecF and (vecvxxvecB)`

Explanation

To solve the problem, we need to identify which pairs of vectors are at right angles to each other based on the given equation for the magnetic force experienced by a charged particle.

### Step-by-Step Solution:

1. **Understanding the Force Equation**:
The force experienced by a charged particle moving in a magnetic field is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
Here, \(\vec{F}\) is the magnetic force, \(q\) is the charge of the particle, \(\vec{v}\) is the velocity vector, and \(\vec{B}\) is the magnetic field vector.

2. **Identifying the Cross Product**:
The expression \(\vec{v} \times \vec{B}\) indicates a cross product. The result of a cross product of two vectors is a vector that is perpendicular to both of the original vectors. Therefore, the vector \(\vec{F}\) is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

3. **Determining the Relationships**:
- Since \(\vec{F}\) is perpendicular to \(\vec{v}\), we can say:
\[ \vec{F} \perp \vec{v} \]
- Similarly, since \(\vec{F}\) is also perpendicular to \(\vec{B}\), we can say:
\[ \vec{F} \perp \vec{B} \]

4. **Conclusion on Pairs of Vectors**:
From the analysis above, we conclude that the pairs of vectors that are at right angles to each other are:
- \(\vec{F}\) and \(\vec{v}\)
- \(\vec{F}\) and \(\vec{B}\)

5. **Final Answer**:
Therefore, the pairs of vectors that are at right angles to each other are:
- \(\vec{F}\) and \(\vec{v}\)
- \(\vec{F}\) and \(\vec{B}\)