A particle of mass $m$ and charge $q$ is positioned at the origin at time $t=0$ .Its initial velocity and initial acceleration are $\vec{v}$ and $\vec{a}$ respectively. There are electric and magnetic fields $\vec{E}$ and $\vec{B}$ throughout space.

How far from the origin is the particle at time $t=15?$

**
Bonus:
**
Plot the trajectories in the
$xy$
,
$yz$
and
$zx$
planes

**
Details and Assumptions
**

**
1)
**
$m=1$

**
2)
**
$q=+2$

**
3)
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$\vec{E} = (E_{x},E_{y},E_{z})=(3,4,5)$

**
4)
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$\vec{B} = (B_{x},B_{y},B_{z})=(6,7,8)$

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5)
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$\vec{v}=(v_{x},v_{y},v_{z})=(9,10,11)$

**
6)
**
$\vec{a}=(a_{x},a_{y},a_{z})=(12,13,14)$

The answer is 1845.732.

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Code-based solution. Done using MATLAB: