A point charge of $100\mu C$ is placed at $\left(3\widehat{i}+4\widehat{j}\right)m.$ Find the electric field intensity due to this charge at a point located at $\left(9\widehat{i}+12\widehat{j}\right)m.$

(2)

$\begin{array}{l}{\overrightarrow{r}}_A=\left(3\widehat{i}+4\widehat{j}\right)m,{\overrightarrow{r}}_B=\left(9\widehat{i}+12\widehat{j}\right)m\\ \therefore {\overrightarrow{r}}_{B/A}={\overrightarrow{r}}_B-{\overrightarrow{r}}_A=\left(6\widehat{i}+8\widehat{j}\right)m\Rightarrow \left|{\overrightarrow{r}}_{B/A}\right|=\sqrt{6^2+8^2}=10m\\ \therefore E_B=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{{\left|{\overrightarrow{r}}_{B/A}\right|}^2}=9\times {10}^9\times \frac{100\times {10}^{-6}}{{\left(10\right)}^2}V/m=9000V/m\end{array}$