In $xY$ cartesian coordinate, three charges $Q,2Q,$ and $2$ Q are placed at position $(0,0),(1,0),$ and

$(0,1),$ respectively. Calculate the net force of these three charges on a test body of charge q

placed at a position $(1,1).$ Here $Q=10C,$ and $q=1C.$

Use coulomb's law, $F=K\frac{Qq}{d^2},$ and principle of superpositoin

$10K\frac{1+4\sqrt[\phantom{2}]{2}}{2}(hat(x)+$hat$(y))$

$10K\frac{1+4\sqrt[\phantom{2}]{2}}{2}(\frac{1}{\sqrt[\phantom{2}]{2}}(hat(x))+\frac{1}{\sqrt[\phantom{2}]{2}}(hat(y)))$

$K\frac{1+4\sqrt[\phantom{2}]{2}}{2}(\frac{1}{\sqrt[\phantom{2}]{2}}(hat(x))+\frac{1}{\sqrt[\phantom{2}]{2}}(hat(y)))$

$10K(\frac{1}{\sqrt[\phantom{2}]{2}}(hat(x))+\frac{1}{\sqrt[\phantom{2}]{2}}(hat(y)))$