A point charge $$50\,\mu C$$  is located in the $$x-y$$  plane at a point whose position vector is $${{\vec r}_0} = \left( {2\hat i + 3\hat j} \right)m.$$    Then electric field at the point whose position vector is $$\vec r = \left( {8\hat i - 5\hat j} \right)m.$$    (in vector form) will be

Solution :
$$\eqalign{ & \vec E = \frac{{kQ}}{{{r^3}}}\vec r = \frac{{9 \times {{10}^9} \times 50 \times {{10}^{ - 6}}}}{{\left| {\vec r - {{\vec r}_0}} \right|}} \times \left( {\vec r - {{\vec r}_0}} \right) \cr & {\text{where}}\,\,\vec r - {{\vec r}_0} = \left( {8\hat i - 5\hat j} \right) - \left( {2\hat i + 3\hat j} \right) = 6\hat i - 8\hat j \cr & \vec E = 900\left( {3\hat i - 4\hat j} \right)V/m \cr} $$