Given two point charges [tex]q_1[/tex] and [tex]q_2[/tex] which are a distance [tex]r_{12}[/tex] apart.
The force [tex]\overrightarrow{F}[/tex] on one of the charges is proportional to the magnitude of its own charge and inversely proportional to the square of the distance between them.
i.e.
[tex]\overrightarrow{F}= \frac{k_e|q_1q_2|}{r_{12}^2} [/tex]
where [tex]k_e[/tex] is the constant of proportionality [tex]8.99\times10^9 \ Nm^2C^{-2}[/tex]
Given that [tex]q_1=2.0\mu C[/tex] and [tex]q_2=4.0\mu C[/tex]
Also, given that [tex]r_ 1 = (4.0i-2.0 j+5.0k)[/tex] m and [tex]r_2 = (8.0 i+ 5.0 j-9.0)[/tex] m, then
[tex]|r_{12}|=|r_2-r_1| \\ \\ =|(8.0 i+ 5.0 j-9.0)-(4.0i-2.0 j+5.0k)| \\ \\ =|4.0i+7.0j-14k|= \sqrt{4^2+7^2+(-14)^2} = \sqrt{16+49+196} \\ \\ = \sqrt{261} =16.2 \ m[/tex]
Therefore, the force of [tex]q_2[/tex] on [tex]q_1[/tex] is given by
[tex]\overrightarrow{F}= \frac{8.99\times10^9\cdot2\times10^{-6}\cdot4\times10^{-6}}{(16.2)^2} \\ \\ = \frac{7.192\times10^{-5}}{261} =2.76\times10^{-7} \ N[/tex]
