(Solved): A proton moves through a uniform magnetic field given by \( \vec{B}=(15.0 \hat{i}-25.4 \hat{j}+12. ...

A proton moves through a uniform magnetic field given by \( \vec{B}=(15.0 \hat{i}-25.4 \hat{j}+12.7 \hat{k}) \mathrm{mT} \). At time \( t_{1} \), the proton has a velocity given by \( \vec{v}=v_{x} \hat{i}+v_{y} \hat{j}+(1.94 \mathrm{~km} / \mathrm{s}) \hat{k} \) and the magnetic force on the proton is \( \vec{F}_{B}=\left(5.33 \times 10^{-17} \mathrm{~N}\right) \hat{i}+\left(3.15 \times 10^{-17} \mathrm{~N}\right) \hat{j} \cdot(\mathrm{a}) \) At that instant, what is \( v_{x} \) ? (b) At that instant, what is \( v_{y} \) ? (a) Number Unit (b) Number Unit eTextbook and Media \begin{tabular}{l|l|} \hline Using multiple attempts will impact your score. & \( \mathrm{m} / \mathrm{s}^{\wedge} 2 \) \\ \( 20 \% \) score reduction after attempt 3 & \( \mathrm{~J} \) \\ & \( \mathrm{~A} \) \\ & \( \mathrm{~A} / \mathrm{m}^{\wedge} 2 \) \\ & \( \mathrm{~A} \bullet \mathrm{m}^{\wedge} 2 \) \\ & \( \mathrm{~T} \) \\ \( \mathrm{~m} \cdot \mathrm{T} / \mathrm{s} \) \\ \( \mathrm{W} \) \\ \hline \end{tabular}