A particle of charge `qgt0` is moving at speed v in the +z direction through a region of uniform magnetic field. The magnetic force on the particle `vec F = F_0 (3 hat i + 4 hat j)`, where `F_0` is a positive constant.
(a) Determine the components `B_x, B_y` and `B_z` or at least as many of the three components as is possible from the information given.
(b) If it is given in addition that the magnetic field has magnitude `6F_0 / (qv)` , determine the magnitude of `B_z`.

Explanation

To solve the problem step by step, we will analyze the given information and apply the relevant physics concepts.

### Step-by-Step Solution:

**Given:**
- A charged particle with charge \( q > 0 \) is moving at speed \( v \) in the \( +z \) direction.
- The magnetic force on the particle is given as \( \vec{F} = F_0 (3 \hat{i} + 4 \hat{j}) \), where \( F_0 \) is a positive constant.
- The magnetic field has components \( B_x, B_y, B_z \).
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