Question Number 79738 by Rio Michael last updated on 27/Jan/20
$${The}\:{forces}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} =\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:{b}\boldsymbol{{j}}\right)\:{N},\:\boldsymbol{{F}}_{\mathrm{2}} =\:\left(−\boldsymbol{{i}}\:+\:\mathrm{2}\boldsymbol{{j}}\right)\:{N} \\ $$$${and}\:\boldsymbol{{F}}_{\mathrm{3}} =\:\left({a}\boldsymbol{{i}}\:−\mathrm{4}\boldsymbol{{j}}\right){N}\:{act}\:{through}\:{the}\:{points}\:{with} \\ $$$${position}\:{vectors}\:\boldsymbol{{r}}_{\mathrm{1}} =\:\left(\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right){m}\:,\boldsymbol{{r}}_{\mathrm{2}} =\left({x}\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\right)\:{m} \\ $$$${and}\:\boldsymbol{{r}}_{\mathrm{3}} =\left(−\boldsymbol{{i}}\:+\:\boldsymbol{{j}}\right){m}\:{respectively}\:. \\ $$$${Given}\:{that}\:{this}\:{system}\:{of}\:{forces}\:{is}\:{equivalent}\:{to}\:{a}\:{couple} \\ $$$${of}\:{magnitude}\:\mathrm{12}\:{N}\:{m},\:{find}\: \\ $$$$\left.{a}\right)\:{the}\:{valueof}\:{the}\:{scalars}\:{a}\:{and}\:{b} \\ $$$$\left.{b}\right)\:{the}\:{possible}\:{values}\:{of}\:{the}\:{scalar}\:{x}. \\ $$