b
\(\vec r\,  = \,\,{{\vec r}_A}\, - \,\,{{\vec r}_B}\,\, = \,\,(\hat i\,\, + \,\,3\hat j\,\, + \,\,2\hat k)\,\, - \,\,(3\hat i\,\, + \,\,5\hat j\,\, + \,\,\hat k)\,\,\)

\(= \,\, - 2\,\,\hat i\,\, - \,\,2\,\,\hat j\,\, + \,\,\hat k\)

\( = \,\,|\vec r|\,\, = \,\,\sqrt {{{(2)}^2}\, + \,\,{{(2)}^2}\, + \,\,{{(1)}^2}} \, = \,\,\sqrt {4\,\,\, + \,\,4\,\, + \,\,1} \,\,\, \)

\(= \,\,\sqrt 9 \,\, = \,\,\,3\ m\)

\(F\,\, = \,\,\frac{{k{q_1}\,\,{q_2}}}{{{r^2}}}\,\, = \,\,\frac{{9\,\, \times \,\,{{10}^9}\, \times \,\,3\,\, \times \,\,{{10}^{ - 6}}\, \times \,\,5\,\, \times \,\,{{10}^{ - 6}}}}{{{{(3)}^2}}}\,\,\, = \,\,1.5\,\, \times \,\,{10^{ - 2}}\,N\)