A magnetic field of $4\times {10}^{-3}\hat{K}\text{T}$ exerts a force of $\left(4\hat{i}+3\hat{j}\right)\times {10}^{-10}\text{N}$ on a particle of charge ${\text{10}}^{-9}\text{C}$ and going in X-Y plane. The velocity of the charged particle is

$\text{let}\overrightarrow{V}=\left(x\hat{i}+y\hat{j}\right){\text{ms}}^{-1}$

$\left(4\hat{i}+3\hat{j}\right)\times {10}^{-10}={10}^{-9}\left(x\hat{i}+y\hat{j}\right)\times 4\times {10}^{-3}\hat{k}$

$\left(4\hat{i}+3\hat{j}\right)=\frac{{10}^{-9}}{{10}^{-10}}\left(-x\hat{i}+y\hat{j}\right)\times 4\times {10}^{-3}$

$4\hat{i}+3\hat{j}=4\times {10}^{-2}\left(y\hat{i}-x\hat{j}\right)$

$4\hat{i}+3\hat{j}=\frac{4}{100}\left(y\hat{i}-x\hat{j}\right)$

$100\hat{i}+75\hat{j}=y\hat{i}-x\hat{j}$

$y=100\text{and}x=-75$

$\overrightarrow{V}=\left(-75\hat{i}+100\hat{j}\right){\text{ms}}^{-1}$