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A uniform and constant magnetic field $\textbf{B}=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass $m$ with a small charge $q$ is introduced into this region with an initial velocity $\textbf{v}=\hat{x}v_{x}+\hat{z}v_{z}$. Given that $B$, $m$, $q$, $v_{x}$ and $v_{z}$ are all non-zero, which one of the following describes the eventual trajectory of the particle?

  1. Helical motion in the $\hat{z}$ direction.
  2. Circular motion in the $xy$ plane.
  3. Linear motion in the $\hat{z}$ direction.
  4. Linear motion in the $\hat{x}$ direction. 
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