Question Number 956 by 123456 last updated on 07/May/15
$$\mathrm{compute}\:\underset{\gamma} {\int}\boldsymbol{{v}}\centerdot{d}\boldsymbol{{r}}\:\mathrm{where} \\ $$$$\boldsymbol{{v}}={yz}\boldsymbol{{i}}+{xz}\boldsymbol{{j}}+{xy}\boldsymbol{{k}} \\ $$$$\mathrm{and}\:\gamma\:\mathrm{is}\:\mathrm{intersection}\:\mathrm{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\:\mathrm{with} \\ $$$${z}={xy}\:\mathrm{orinted}\:\mathrm{in}\:\mathrm{the}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{prpjection}\:\mathrm{on}\:{xy}\:\mathrm{travel}\:\mathrm{by}\:\circlearrowleft \\ $$