A charged particle has acceleration `vec a = 2 hat i + x hat j ` in a megnetic field `vec B = - 3 hat i + 2 hat j - 4 hat k.` Find the value of x.

Explanation

To solve the problem, we need to find the value of \( x \) given the acceleration vector \( \vec{a} = 2 \hat{i} + x \hat{j} \) and the magnetic field vector \( \vec{B} = -3 \hat{i} + 2 \hat{j} - 4 \hat{k} \).

### Step-by-Step Solution:

1. **Understand the relationship between acceleration and magnetic field**:
The force on a charged particle in a magnetic field is given by the Lorentz force law, which states that the magnetic force \( \vec{F} \) is given by \( \vec{F} = q(\vec{v} \times \vec{B}) \). The acceleration \( \vec{a} \) of the particle is related to the force by Newton's second law \( \vec{F} = m \vec{a} \).

2. **Recognize that acceleration is perpendicular to the magnetic field**:
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