#### Arman777

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**1. The problem statement, all variables and given/known data**

Solve the Lorentz Force Equation (Find ##\vec{r}(t)##) under constant ##\vec {B}## and ##\vec {E}##.

İnitial Velocity: ##\vec{v_i}=<0,0,0>##

İnitial position: ##\vec{r_i}=<0,0,0>##

(##\vec {B}## and ##\vec {E}## are given values)

**2. Relevant equations**

Lorentz Force:

##\vec {F}=q(\vec {E}+\vec{v} × \vec {B})##

**3. The attempt at a solution**

So I write the equaiton in a diff eqn form like,

##m\vec{a}=q(\vec {E}+\vec{v} × \vec {B})##

then

##\ddot {\vec{r}}-\frac {q} {m}(\dot {\vec{r}}× \vec {B})=\frac {q\vec {E}} {m}##

Now the right side is constant and left side have also constant coefficients. I am not sure how to proceed after this. I can use auxiliary equation maybe ? but since these equations are about vectors I am not sure how would that work out.

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